Help the biographer complete the dramatic turning point of the inventor's life. Choose the correct phrase.

Arthur confidently unveiled his self-buttering toaster to the investors, completely unaware that this spectacular malfunction ______ him his entire career.

The correct answer is would cost.

We use would + base verb to express the "future in the past"—specifically to talk about a destiny or the final outcome of a past situation, viewed from that point in the past. Because the main narrative is in the past ("unveiled," "unaware"), the future consequence ("will cost") must shift back to "would cost."