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Simplifying x * x + 20x = 71 Multiply x * x x2 + 20x = 71 Reorder the terms: 20x + x2 = 71 Solving 20x + x2 = 71 Solving for variable 'x'. Reorder the terms: -71 + 20x + x2 = 71 + -71 Combine like terms: 71 + -71 = 0 -71 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '71' to each side of the equation. -71 + 20x + 71 + x2 = 0 + 71 Reorder the terms: -71 + 71 + 20x + x2 = 0 + 71 Combine like terms: -71 + 71 = 0 0 + 20x + x2 = 0 + 71 20x + x2 = 0 + 71 Combine like terms: 0 + 71 = 71 20x + x2 = 71 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 = 71 + 100 Reorder the terms: 100 + 20x + x2 = 71 + 100 Combine like terms: 71 + 100 = 171 100 + 20x + x2 = 171 Factor a perfect square on the left side: (x + 10)(x + 10) = 171 Calculate the square root of the right side: 13.076696831 Break this problem into two subproblems by setting (x + 10) equal to 13.076696831 and -13.076696831.Subproblem 1
x + 10 = 13.076696831 Simplifying x + 10 = 13.076696831 Reorder the terms: 10 + x = 13.076696831 Solving 10 + x = 13.076696831 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 = 13.076696831 + -10 Combine like terms: 10 + -10 = 0 0 + x = 13.076696831 + -10 x = 13.076696831 + -10 Combine like terms: 13.076696831 + -10 = 3.076696831 x = 3.076696831 Simplifying x = 3.076696831Subproblem 2
x + 10 = -13.076696831 Simplifying x + 10 = -13.076696831 Reorder the terms: 10 + x = -13.076696831 Solving 10 + x = -13.076696831 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 = -13.076696831 + -10 Combine like terms: 10 + -10 = 0 0 + x = -13.076696831 + -10 x = -13.076696831 + -10 Combine like terms: -13.076696831 + -10 = -23.076696831 x = -23.076696831 Simplifying x = -23.076696831Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.076696831, -23.076696831}
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