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Simplifying x * x + -4x = 90 Multiply x * x x2 + -4x = 90 Reorder the terms: -4x + x2 = 90 Solving -4x + x2 = 90 Solving for variable 'x'. Reorder the terms: -90 + -4x + x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + -4x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + -4x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -4x + x2 = 0 + 90 -4x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 -4x + x2 = 90 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 90 + 4 Reorder the terms: 4 + -4x + x2 = 90 + 4 Combine like terms: 90 + 4 = 94 4 + -4x + x2 = 94 Factor a perfect square on the left side: (x + -2)(x + -2) = 94 Calculate the square root of the right side: 9.695359715 Break this problem into two subproblems by setting (x + -2) equal to 9.695359715 and -9.695359715.Subproblem 1
x + -2 = 9.695359715 Simplifying x + -2 = 9.695359715 Reorder the terms: -2 + x = 9.695359715 Solving -2 + x = 9.695359715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 9.695359715 + 2 Combine like terms: -2 + 2 = 0 0 + x = 9.695359715 + 2 x = 9.695359715 + 2 Combine like terms: 9.695359715 + 2 = 11.695359715 x = 11.695359715 Simplifying x = 11.695359715Subproblem 2
x + -2 = -9.695359715 Simplifying x + -2 = -9.695359715 Reorder the terms: -2 + x = -9.695359715 Solving -2 + x = -9.695359715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -9.695359715 + 2 Combine like terms: -2 + 2 = 0 0 + x = -9.695359715 + 2 x = -9.695359715 + 2 Combine like terms: -9.695359715 + 2 = -7.695359715 x = -7.695359715 Simplifying x = -7.695359715Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.695359715, -7.695359715}
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