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Simplifying (x + -9)(x + -9) = 10 Reorder the terms: (-9 + x)(x + -9) = 10 Reorder the terms: (-9 + x)(-9 + x) = 10 Multiply (-9 + x) * (-9 + x) (-9(-9 + x) + x(-9 + x)) = 10 ((-9 * -9 + x * -9) + x(-9 + x)) = 10 ((81 + -9x) + x(-9 + x)) = 10 (81 + -9x + (-9 * x + x * x)) = 10 (81 + -9x + (-9x + x2)) = 10 Combine like terms: -9x + -9x = -18x (81 + -18x + x2) = 10 Solving 81 + -18x + x2 = 10 Solving for variable 'x'. Reorder the terms: 81 + -10 + -18x + x2 = 10 + -10 Combine like terms: 81 + -10 = 71 71 + -18x + x2 = 10 + -10 Combine like terms: 10 + -10 = 0 71 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-71' to each side of the equation. 71 + -18x + -71 + x2 = 0 + -71 Reorder the terms: 71 + -71 + -18x + x2 = 0 + -71 Combine like terms: 71 + -71 = 0 0 + -18x + x2 = 0 + -71 -18x + x2 = 0 + -71 Combine like terms: 0 + -71 = -71 -18x + x2 = -71 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = -71 + 81 Reorder the terms: 81 + -18x + x2 = -71 + 81 Combine like terms: -71 + 81 = 10 81 + -18x + x2 = 10 Factor a perfect square on the left side: (x + -9)(x + -9) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x + -9) equal to 3.16227766 and -3.16227766.Subproblem 1
x + -9 = 3.16227766 Simplifying x + -9 = 3.16227766 Reorder the terms: -9 + x = 3.16227766 Solving -9 + x = 3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 3.16227766 + 9 Combine like terms: -9 + 9 = 0 0 + x = 3.16227766 + 9 x = 3.16227766 + 9 Combine like terms: 3.16227766 + 9 = 12.16227766 x = 12.16227766 Simplifying x = 12.16227766Subproblem 2
x + -9 = -3.16227766 Simplifying x + -9 = -3.16227766 Reorder the terms: -9 + x = -3.16227766 Solving -9 + x = -3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -3.16227766 + 9 Combine like terms: -9 + 9 = 0 0 + x = -3.16227766 + 9 x = -3.16227766 + 9 Combine like terms: -3.16227766 + 9 = 5.83772234 x = 5.83772234 Simplifying x = 5.83772234Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.16227766, 5.83772234}
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