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Simplifying x * x + 8x = 90 Multiply x * x x2 + 8x = 90 Reorder the terms: 8x + x2 = 90 Solving 8x + x2 = 90 Solving for variable 'x'. Reorder the terms: -90 + 8x + x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + 8x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 8x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 8x + x2 = 0 + 90 8x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 8x + x2 = 90 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 90 + 16 Reorder the terms: 16 + 8x + x2 = 90 + 16 Combine like terms: 90 + 16 = 106 16 + 8x + x2 = 106 Factor a perfect square on the left side: (x + 4)(x + 4) = 106 Calculate the square root of the right side: 10.295630141 Break this problem into two subproblems by setting (x + 4) equal to 10.295630141 and -10.295630141.Subproblem 1
x + 4 = 10.295630141 Simplifying x + 4 = 10.295630141 Reorder the terms: 4 + x = 10.295630141 Solving 4 + x = 10.295630141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 10.295630141 + -4 Combine like terms: 4 + -4 = 0 0 + x = 10.295630141 + -4 x = 10.295630141 + -4 Combine like terms: 10.295630141 + -4 = 6.295630141 x = 6.295630141 Simplifying x = 6.295630141Subproblem 2
x + 4 = -10.295630141 Simplifying x + 4 = -10.295630141 Reorder the terms: 4 + x = -10.295630141 Solving 4 + x = -10.295630141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -10.295630141 + -4 Combine like terms: 4 + -4 = 0 0 + x = -10.295630141 + -4 x = -10.295630141 + -4 Combine like terms: -10.295630141 + -4 = -14.295630141 x = -14.295630141 Simplifying x = -14.295630141Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.295630141, -14.295630141}
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