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Simplifying x(-2x + 18) + -35 = 0 Reorder the terms: x(18 + -2x) + -35 = 0 (18 * x + -2x * x) + -35 = 0 (18x + -2x2) + -35 = 0 Reorder the terms: -35 + 18x + -2x2 = 0 Solving -35 + 18x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 17.5 + -9x + x2 = 0 Move the constant term to the right: Add '-17.5' to each side of the equation. 17.5 + -9x + -17.5 + x2 = 0 + -17.5 Reorder the terms: 17.5 + -17.5 + -9x + x2 = 0 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + -9x + x2 = 0 + -17.5 -9x + x2 = 0 + -17.5 Combine like terms: 0 + -17.5 = -17.5 -9x + x2 = -17.5 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = -17.5 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -17.5 + 20.25 Combine like terms: -17.5 + 20.25 = 2.75 20.25 + -9x + x2 = 2.75 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (x + -4.5) equal to 1.658312395 and -1.658312395.Subproblem 1
x + -4.5 = 1.658312395 Simplifying x + -4.5 = 1.658312395 Reorder the terms: -4.5 + x = 1.658312395 Solving -4.5 + x = 1.658312395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 1.658312395 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 1.658312395 + 4.5 x = 1.658312395 + 4.5 Combine like terms: 1.658312395 + 4.5 = 6.158312395 x = 6.158312395 Simplifying x = 6.158312395Subproblem 2
x + -4.5 = -1.658312395 Simplifying x + -4.5 = -1.658312395 Reorder the terms: -4.5 + x = -1.658312395 Solving -4.5 + x = -1.658312395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -1.658312395 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -1.658312395 + 4.5 x = -1.658312395 + 4.5 Combine like terms: -1.658312395 + 4.5 = 2.841687605 x = 2.841687605 Simplifying x = 2.841687605Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.158312395, 2.841687605}
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