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Simplifying 100 + -90 = x2 + 20x + 100 Combine like terms: 100 + -90 = 10 10 = x2 + 20x + 100 Reorder the terms: 10 = 100 + 20x + x2 Solving 10 = 100 + 20x + x2 Solving for variable 'x'. Combine like terms: 10 + -100 = -90 -90 + -20x + -1x2 = 100 + 20x + x2 + -100 + -20x + -1x2 Reorder the terms: -90 + -20x + -1x2 = 100 + -100 + 20x + -20x + x2 + -1x2 Combine like terms: 100 + -100 = 0 -90 + -20x + -1x2 = 0 + 20x + -20x + x2 + -1x2 -90 + -20x + -1x2 = 20x + -20x + x2 + -1x2 Combine like terms: 20x + -20x = 0 -90 + -20x + -1x2 = 0 + x2 + -1x2 -90 + -20x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -90 + -20x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(90 + 20x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(90 + 20x + x2)' equal to zero and attempt to solve: Simplifying 90 + 20x + x2 = 0 Solving 90 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-90' to each side of the equation. 90 + 20x + -90 + x2 = 0 + -90 Reorder the terms: 90 + -90 + 20x + x2 = 0 + -90 Combine like terms: 90 + -90 = 0 0 + 20x + x2 = 0 + -90 20x + x2 = 0 + -90 Combine like terms: 0 + -90 = -90 20x + x2 = -90 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = -90 + 100 Reorder the terms: 100 + 20x + x2 = -90 + 100 Combine like terms: -90 + 100 = 10 100 + 20x + x2 = 10 Factor a perfect square on the left side: (x + 10)(x + 10) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x + 10) equal to 3.16227766 and -3.16227766.Subproblem 1
x + 10 = 3.16227766 Simplifying x + 10 = 3.16227766 Reorder the terms: 10 + x = 3.16227766 Solving 10 + x = 3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 3.16227766 + -10 Combine like terms: 10 + -10 = 0 0 + x = 3.16227766 + -10 x = 3.16227766 + -10 Combine like terms: 3.16227766 + -10 = -6.83772234 x = -6.83772234 Simplifying x = -6.83772234Subproblem 2
x + 10 = -3.16227766 Simplifying x + 10 = -3.16227766 Reorder the terms: 10 + x = -3.16227766 Solving 10 + x = -3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -3.16227766 + -10 Combine like terms: 10 + -10 = 0 0 + x = -3.16227766 + -10 x = -3.16227766 + -10 Combine like terms: -3.16227766 + -10 = -13.16227766 x = -13.16227766 Simplifying x = -13.16227766Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.83772234, -13.16227766}Solution
x = {-6.83772234, -13.16227766}
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