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Simplifying 1358 = x2 + -17x Reorder the terms: 1358 = -17x + x2 Solving 1358 = -17x + x2 Solving for variable 'x'. Reorder the terms: 1358 + 17x + -1x2 = -17x + 17x + x2 + -1x2 Combine like terms: -17x + 17x = 0 1358 + 17x + -1x2 = 0 + x2 + -1x2 1358 + 17x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 1358 + 17x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1358 + -17x + x2 = 0 Move the constant term to the right: Add '1358' to each side of the equation. -1358 + -17x + 1358 + x2 = 0 + 1358 Reorder the terms: -1358 + 1358 + -17x + x2 = 0 + 1358 Combine like terms: -1358 + 1358 = 0 0 + -17x + x2 = 0 + 1358 -17x + x2 = 0 + 1358 Combine like terms: 0 + 1358 = 1358 -17x + x2 = 1358 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = 1358 + 72.25 Reorder the terms: 72.25 + -17x + x2 = 1358 + 72.25 Combine like terms: 1358 + 72.25 = 1430.25 72.25 + -17x + x2 = 1430.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 1430.25 Calculate the square root of the right side: 37.818646195 Break this problem into two subproblems by setting (x + -8.5) equal to 37.818646195 and -37.818646195.Subproblem 1
x + -8.5 = 37.818646195 Simplifying x + -8.5 = 37.818646195 Reorder the terms: -8.5 + x = 37.818646195 Solving -8.5 + x = 37.818646195 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 37.818646195 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 37.818646195 + 8.5 x = 37.818646195 + 8.5 Combine like terms: 37.818646195 + 8.5 = 46.318646195 x = 46.318646195 Simplifying x = 46.318646195Subproblem 2
x + -8.5 = -37.818646195 Simplifying x + -8.5 = -37.818646195 Reorder the terms: -8.5 + x = -37.818646195 Solving -8.5 + x = -37.818646195 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -37.818646195 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -37.818646195 + 8.5 x = -37.818646195 + 8.5 Combine like terms: -37.818646195 + 8.5 = -29.318646195 x = -29.318646195 Simplifying x = -29.318646195Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.318646195, -29.318646195}
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