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Simplifying x2 + 19x + -70 = 0 Reorder the terms: -70 + 19x + x2 = 0 Solving -70 + 19x + 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 + 19x + 70 + x2 = 0 + 70 Reorder the terms: -70 + 70 + 19x + x2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + 19x + x2 = 0 + 70 19x + x2 = 0 + 70 Combine like terms: 0 + 70 = 70 19x + x2 = 70 The x term is 19x. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19x + 90.25 + x2 = 70 + 90.25 Reorder the terms: 90.25 + 19x + x2 = 70 + 90.25 Combine like terms: 70 + 90.25 = 160.25 90.25 + 19x + x2 = 160.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 160.25 Calculate the square root of the right side: 12.658988901 Break this problem into two subproblems by setting (x + 9.5) equal to 12.658988901 and -12.658988901.Subproblem 1
x + 9.5 = 12.658988901 Simplifying x + 9.5 = 12.658988901 Reorder the terms: 9.5 + x = 12.658988901 Solving 9.5 + x = 12.658988901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = 12.658988901 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 12.658988901 + -9.5 x = 12.658988901 + -9.5 Combine like terms: 12.658988901 + -9.5 = 3.158988901 x = 3.158988901 Simplifying x = 3.158988901Subproblem 2
x + 9.5 = -12.658988901 Simplifying x + 9.5 = -12.658988901 Reorder the terms: 9.5 + x = -12.658988901 Solving 9.5 + x = -12.658988901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = -12.658988901 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -12.658988901 + -9.5 x = -12.658988901 + -9.5 Combine like terms: -12.658988901 + -9.5 = -22.158988901 x = -22.158988901 Simplifying x = -22.158988901Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.158988901, -22.158988901}
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