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Simplifying 72 = 5x2 + -4x + -40 Reorder the terms: 72 = -40 + -4x + 5x2 Solving 72 = -40 + -4x + 5x2 Solving for variable 'x'. Combine like terms: 72 + 40 = 112 112 + 4x + -5x2 = -40 + -4x + 5x2 + 40 + 4x + -5x2 Reorder the terms: 112 + 4x + -5x2 = -40 + 40 + -4x + 4x + 5x2 + -5x2 Combine like terms: -40 + 40 = 0 112 + 4x + -5x2 = 0 + -4x + 4x + 5x2 + -5x2 112 + 4x + -5x2 = -4x + 4x + 5x2 + -5x2 Combine like terms: -4x + 4x = 0 112 + 4x + -5x2 = 0 + 5x2 + -5x2 112 + 4x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 112 + 4x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -22.4 + -0.8x + x2 = 0 Move the constant term to the right: Add '22.4' to each side of the equation. -22.4 + -0.8x + 22.4 + x2 = 0 + 22.4 Reorder the terms: -22.4 + 22.4 + -0.8x + x2 = 0 + 22.4 Combine like terms: -22.4 + 22.4 = 0.0 0.0 + -0.8x + x2 = 0 + 22.4 -0.8x + x2 = 0 + 22.4 Combine like terms: 0 + 22.4 = 22.4 -0.8x + x2 = 22.4 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 22.4 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 22.4 + 0.16 Combine like terms: 22.4 + 0.16 = 22.56 0.16 + -0.8x + x2 = 22.56 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 22.56 Calculate the square root of the right side: 4.749736835 Break this problem into two subproblems by setting (x + -0.4) equal to 4.749736835 and -4.749736835.Subproblem 1
x + -0.4 = 4.749736835 Simplifying x + -0.4 = 4.749736835 Reorder the terms: -0.4 + x = 4.749736835 Solving -0.4 + x = 4.749736835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 4.749736835 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 4.749736835 + 0.4 x = 4.749736835 + 0.4 Combine like terms: 4.749736835 + 0.4 = 5.149736835 x = 5.149736835 Simplifying x = 5.149736835Subproblem 2
x + -0.4 = -4.749736835 Simplifying x + -0.4 = -4.749736835 Reorder the terms: -0.4 + x = -4.749736835 Solving -0.4 + x = -4.749736835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -4.749736835 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -4.749736835 + 0.4 x = -4.749736835 + 0.4 Combine like terms: -4.749736835 + 0.4 = -4.349736835 x = -4.349736835 Simplifying x = -4.349736835Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.149736835, -4.349736835}
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