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Simplifying 4x = x2 + -70 Reorder the terms: 4x = -70 + x2 Solving 4x = -70 + x2 Solving for variable 'x'. Reorder the terms: 70 + 4x + -1x2 = -70 + x2 + 70 + -1x2 Reorder the terms: 70 + 4x + -1x2 = -70 + 70 + x2 + -1x2 Combine like terms: -70 + 70 = 0 70 + 4x + -1x2 = 0 + x2 + -1x2 70 + 4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 70 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -70 + -4x + x2 = 0 Move the constant term to the right: Add '70' to each side of the equation. -70 + -4x + 70 + x2 = 0 + 70 Reorder the terms: -70 + 70 + -4x + x2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + -4x + x2 = 0 + 70 -4x + x2 = 0 + 70 Combine like terms: 0 + 70 = 70 -4x + x2 = 70 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 = 70 + 4 Reorder the terms: 4 + -4x + x2 = 70 + 4 Combine like terms: 70 + 4 = 74 4 + -4x + x2 = 74 Factor a perfect square on the left side: (x + -2)(x + -2) = 74 Calculate the square root of the right side: 8.602325267 Break this problem into two subproblems by setting (x + -2) equal to 8.602325267 and -8.602325267.Subproblem 1
x + -2 = 8.602325267 Simplifying x + -2 = 8.602325267 Reorder the terms: -2 + x = 8.602325267 Solving -2 + x = 8.602325267 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 = 8.602325267 + 2 Combine like terms: -2 + 2 = 0 0 + x = 8.602325267 + 2 x = 8.602325267 + 2 Combine like terms: 8.602325267 + 2 = 10.602325267 x = 10.602325267 Simplifying x = 10.602325267Subproblem 2
x + -2 = -8.602325267 Simplifying x + -2 = -8.602325267 Reorder the terms: -2 + x = -8.602325267 Solving -2 + x = -8.602325267 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 = -8.602325267 + 2 Combine like terms: -2 + 2 = 0 0 + x = -8.602325267 + 2 x = -8.602325267 + 2 Combine like terms: -8.602325267 + 2 = -6.602325267 x = -6.602325267 Simplifying x = -6.602325267Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.602325267, -6.602325267}
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