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Simplifying 0.5x2 + 2x + -70 = 0 Reorder the terms: -70 + 2x + 0.5x2 = 0 Solving -70 + 2x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -140 + 4x + x2 = 0 Move the constant term to the right: Add '140' to each side of the equation. -140 + 4x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + 4x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + 4x + x2 = 0 + 140 4x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 4x + x2 = 140 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 140 + 4 Reorder the terms: 4 + 4x + x2 = 140 + 4 Combine like terms: 140 + 4 = 144 4 + 4x + x2 = 144 Factor a perfect square on the left side: (x + 2)(x + 2) = 144 Calculate the square root of the right side: 12 Break this problem into two subproblems by setting (x + 2) equal to 12 and -12.Subproblem 1
x + 2 = 12 Simplifying x + 2 = 12 Reorder the terms: 2 + x = 12 Solving 2 + x = 12 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 12 + -2 Combine like terms: 2 + -2 = 0 0 + x = 12 + -2 x = 12 + -2 Combine like terms: 12 + -2 = 10 x = 10 Simplifying x = 10Subproblem 2
x + 2 = -12 Simplifying x + 2 = -12 Reorder the terms: 2 + x = -12 Solving 2 + x = -12 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -12 + -2 Combine like terms: 2 + -2 = 0 0 + x = -12 + -2 x = -12 + -2 Combine like terms: -12 + -2 = -14 x = -14 Simplifying x = -14Solution
The solution to the problem is based on the solutions from the subproblems. x = {10, -14}
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