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Simplifying x2 + -24x + 70 = 0 Reorder the terms: 70 + -24x + x2 = 0 Solving 70 + -24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-70' to each side of the equation. 70 + -24x + -70 + x2 = 0 + -70 Reorder the terms: 70 + -70 + -24x + x2 = 0 + -70 Combine like terms: 70 + -70 = 0 0 + -24x + x2 = 0 + -70 -24x + x2 = 0 + -70 Combine like terms: 0 + -70 = -70 -24x + x2 = -70 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = -70 + 144 Reorder the terms: 144 + -24x + x2 = -70 + 144 Combine like terms: -70 + 144 = 74 144 + -24x + x2 = 74 Factor a perfect square on the left side: (x + -12)(x + -12) = 74 Calculate the square root of the right side: 8.602325267 Break this problem into two subproblems by setting (x + -12) equal to 8.602325267 and -8.602325267.Subproblem 1
x + -12 = 8.602325267 Simplifying x + -12 = 8.602325267 Reorder the terms: -12 + x = 8.602325267 Solving -12 + x = 8.602325267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 8.602325267 + 12 Combine like terms: -12 + 12 = 0 0 + x = 8.602325267 + 12 x = 8.602325267 + 12 Combine like terms: 8.602325267 + 12 = 20.602325267 x = 20.602325267 Simplifying x = 20.602325267Subproblem 2
x + -12 = -8.602325267 Simplifying x + -12 = -8.602325267 Reorder the terms: -12 + x = -8.602325267 Solving -12 + x = -8.602325267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -8.602325267 + 12 Combine like terms: -12 + 12 = 0 0 + x = -8.602325267 + 12 x = -8.602325267 + 12 Combine like terms: -8.602325267 + 12 = 3.397674733 x = 3.397674733 Simplifying x = 3.397674733Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.602325267, 3.397674733}
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