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Simplifying 70 + -52x = -1x2 Solving 70 + -52x = -1x2 Solving for variable 'x'. Combine like terms: -1x2 + x2 = 0 70 + -52x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-70' to each side of the equation. 70 + -52x + -70 + x2 = 0 + -70 Reorder the terms: 70 + -70 + -52x + x2 = 0 + -70 Combine like terms: 70 + -70 = 0 0 + -52x + x2 = 0 + -70 -52x + x2 = 0 + -70 Combine like terms: 0 + -70 = -70 -52x + x2 = -70 The x term is -52x. Take half its coefficient (-26). Square it (676) and add it to both sides. Add '676' to each side of the equation. -52x + 676 + x2 = -70 + 676 Reorder the terms: 676 + -52x + x2 = -70 + 676 Combine like terms: -70 + 676 = 606 676 + -52x + x2 = 606 Factor a perfect square on the left side: (x + -26)(x + -26) = 606 Calculate the square root of the right side: 24.61706725 Break this problem into two subproblems by setting (x + -26) equal to 24.61706725 and -24.61706725.Subproblem 1
x + -26 = 24.61706725 Simplifying x + -26 = 24.61706725 Reorder the terms: -26 + x = 24.61706725 Solving -26 + x = 24.61706725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26' to each side of the equation. -26 + 26 + x = 24.61706725 + 26 Combine like terms: -26 + 26 = 0 0 + x = 24.61706725 + 26 x = 24.61706725 + 26 Combine like terms: 24.61706725 + 26 = 50.61706725 x = 50.61706725 Simplifying x = 50.61706725Subproblem 2
x + -26 = -24.61706725 Simplifying x + -26 = -24.61706725 Reorder the terms: -26 + x = -24.61706725 Solving -26 + x = -24.61706725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26' to each side of the equation. -26 + 26 + x = -24.61706725 + 26 Combine like terms: -26 + 26 = 0 0 + x = -24.61706725 + 26 x = -24.61706725 + 26 Combine like terms: -24.61706725 + 26 = 1.38293275 x = 1.38293275 Simplifying x = 1.38293275Solution
The solution to the problem is based on the solutions from the subproblems. x = {50.61706725, 1.38293275}
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