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Simplifying 10 + x + x + x2 = 180 Combine like terms: x + x = 2x 10 + 2x + x2 = 180 Solving 10 + 2x + x2 = 180 Solving for variable 'x'. Reorder the terms: 10 + -180 + 2x + x2 = 180 + -180 Combine like terms: 10 + -180 = -170 -170 + 2x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -170 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '170' to each side of the equation. -170 + 2x + 170 + x2 = 0 + 170 Reorder the terms: -170 + 170 + 2x + x2 = 0 + 170 Combine like terms: -170 + 170 = 0 0 + 2x + x2 = 0 + 170 2x + x2 = 0 + 170 Combine like terms: 0 + 170 = 170 2x + x2 = 170 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 170 + 1 Reorder the terms: 1 + 2x + x2 = 170 + 1 Combine like terms: 170 + 1 = 171 1 + 2x + x2 = 171 Factor a perfect square on the left side: (x + 1)(x + 1) = 171 Calculate the square root of the right side: 13.076696831 Break this problem into two subproblems by setting (x + 1) equal to 13.076696831 and -13.076696831.Subproblem 1
x + 1 = 13.076696831 Simplifying x + 1 = 13.076696831 Reorder the terms: 1 + x = 13.076696831 Solving 1 + x = 13.076696831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 13.076696831 + -1 Combine like terms: 1 + -1 = 0 0 + x = 13.076696831 + -1 x = 13.076696831 + -1 Combine like terms: 13.076696831 + -1 = 12.076696831 x = 12.076696831 Simplifying x = 12.076696831Subproblem 2
x + 1 = -13.076696831 Simplifying x + 1 = -13.076696831 Reorder the terms: 1 + x = -13.076696831 Solving 1 + x = -13.076696831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -13.076696831 + -1 Combine like terms: 1 + -1 = 0 0 + x = -13.076696831 + -1 x = -13.076696831 + -1 Combine like terms: -13.076696831 + -1 = -14.076696831 x = -14.076696831 Simplifying x = -14.076696831Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.076696831, -14.076696831}
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