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Simplifying 7x = x2 + -70 Reorder the terms: 7x = -70 + x2 Solving 7x = -70 + x2 Solving for variable 'x'. Reorder the terms: 70 + 7x + -1x2 = -70 + x2 + 70 + -1x2 Reorder the terms: 70 + 7x + -1x2 = -70 + 70 + x2 + -1x2 Combine like terms: -70 + 70 = 0 70 + 7x + -1x2 = 0 + x2 + -1x2 70 + 7x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 70 + 7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -70 + -7x + x2 = 0 Move the constant term to the right: Add '70' to each side of the equation. -70 + -7x + 70 + x2 = 0 + 70 Reorder the terms: -70 + 70 + -7x + x2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + -7x + x2 = 0 + 70 -7x + x2 = 0 + 70 Combine like terms: 0 + 70 = 70 -7x + x2 = 70 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 70 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 70 + 12.25 Combine like terms: 70 + 12.25 = 82.25 12.25 + -7x + x2 = 82.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 82.25 Calculate the square root of the right side: 9.069178574 Break this problem into two subproblems by setting (x + -3.5) equal to 9.069178574 and -9.069178574.Subproblem 1
x + -3.5 = 9.069178574 Simplifying x + -3.5 = 9.069178574 Reorder the terms: -3.5 + x = 9.069178574 Solving -3.5 + x = 9.069178574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 9.069178574 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 9.069178574 + 3.5 x = 9.069178574 + 3.5 Combine like terms: 9.069178574 + 3.5 = 12.569178574 x = 12.569178574 Simplifying x = 12.569178574Subproblem 2
x + -3.5 = -9.069178574 Simplifying x + -3.5 = -9.069178574 Reorder the terms: -3.5 + x = -9.069178574 Solving -3.5 + x = -9.069178574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -9.069178574 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -9.069178574 + 3.5 x = -9.069178574 + 3.5 Combine like terms: -9.069178574 + 3.5 = -5.569178574 x = -5.569178574 Simplifying x = -5.569178574Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.569178574, -5.569178574}
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