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Simplifying 3.91x2 + -10.45x + 4.42 = 0 Reorder the terms: 4.42 + -10.45x + 3.91x2 = 0 Solving 4.42 + -10.45x + 3.91x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.91 the coefficient of the squared term: Divide each side by '3.91'. 1.130434783 + -2.672634271x + x2 = 0 Move the constant term to the right: Add '-1.130434783' to each side of the equation. 1.130434783 + -2.672634271x + -1.130434783 + x2 = 0 + -1.130434783 Reorder the terms: 1.130434783 + -1.130434783 + -2.672634271x + x2 = 0 + -1.130434783 Combine like terms: 1.130434783 + -1.130434783 = 0.000000000 0.000000000 + -2.672634271x + x2 = 0 + -1.130434783 -2.672634271x + x2 = 0 + -1.130434783 Combine like terms: 0 + -1.130434783 = -1.130434783 -2.672634271x + x2 = -1.130434783 The x term is -2.672634271x. Take half its coefficient (-1.336317136). Square it (1.785743488) and add it to both sides. Add '1.785743488' to each side of the equation. -2.672634271x + 1.785743488 + x2 = -1.130434783 + 1.785743488 Reorder the terms: 1.785743488 + -2.672634271x + x2 = -1.130434783 + 1.785743488 Combine like terms: -1.130434783 + 1.785743488 = 0.655308705 1.785743488 + -2.672634271x + x2 = 0.655308705 Factor a perfect square on the left side: (x + -1.336317136)(x + -1.336317136) = 0.655308705 Calculate the square root of the right side: 0.809511399 Break this problem into two subproblems by setting (x + -1.336317136) equal to 0.809511399 and -0.809511399.Subproblem 1
x + -1.336317136 = 0.809511399 Simplifying x + -1.336317136 = 0.809511399 Reorder the terms: -1.336317136 + x = 0.809511399 Solving -1.336317136 + x = 0.809511399 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.336317136' to each side of the equation. -1.336317136 + 1.336317136 + x = 0.809511399 + 1.336317136 Combine like terms: -1.336317136 + 1.336317136 = 0.000000000 0.000000000 + x = 0.809511399 + 1.336317136 x = 0.809511399 + 1.336317136 Combine like terms: 0.809511399 + 1.336317136 = 2.145828535 x = 2.145828535 Simplifying x = 2.145828535Subproblem 2
x + -1.336317136 = -0.809511399 Simplifying x + -1.336317136 = -0.809511399 Reorder the terms: -1.336317136 + x = -0.809511399 Solving -1.336317136 + x = -0.809511399 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.336317136' to each side of the equation. -1.336317136 + 1.336317136 + x = -0.809511399 + 1.336317136 Combine like terms: -1.336317136 + 1.336317136 = 0.000000000 0.000000000 + x = -0.809511399 + 1.336317136 x = -0.809511399 + 1.336317136 Combine like terms: -0.809511399 + 1.336317136 = 0.526805737 x = 0.526805737 Simplifying x = 0.526805737Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.145828535, 0.526805737}
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