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Simplifying -14x2 + 1260x + -1120 = 0 Reorder the terms: -1120 + 1260x + -14x2 = 0 Solving -1120 + 1260x + -14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '14'. 14(-80 + 90x + -1x2) = 0 Ignore the factor 14.Subproblem 1
Set the factor '(-80 + 90x + -1x2)' equal to zero and attempt to solve: Simplifying -80 + 90x + -1x2 = 0 Solving -80 + 90x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 80 + -90x + x2 = 0 Move the constant term to the right: Add '-80' to each side of the equation. 80 + -90x + -80 + x2 = 0 + -80 Reorder the terms: 80 + -80 + -90x + x2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + -90x + x2 = 0 + -80 -90x + x2 = 0 + -80 Combine like terms: 0 + -80 = -80 -90x + x2 = -80 The x term is -90x. Take half its coefficient (-45). Square it (2025) and add it to both sides. Add '2025' to each side of the equation. -90x + 2025 + x2 = -80 + 2025 Reorder the terms: 2025 + -90x + x2 = -80 + 2025 Combine like terms: -80 + 2025 = 1945 2025 + -90x + x2 = 1945 Factor a perfect square on the left side: (x + -45)(x + -45) = 1945 Calculate the square root of the right side: 44.102154142 Break this problem into two subproblems by setting (x + -45) equal to 44.102154142 and -44.102154142.Subproblem 1
x + -45 = 44.102154142 Simplifying x + -45 = 44.102154142 Reorder the terms: -45 + x = 44.102154142 Solving -45 + x = 44.102154142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + x = 44.102154142 + 45 Combine like terms: -45 + 45 = 0 0 + x = 44.102154142 + 45 x = 44.102154142 + 45 Combine like terms: 44.102154142 + 45 = 89.102154142 x = 89.102154142 Simplifying x = 89.102154142Subproblem 2
x + -45 = -44.102154142 Simplifying x + -45 = -44.102154142 Reorder the terms: -45 + x = -44.102154142 Solving -45 + x = -44.102154142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + x = -44.102154142 + 45 Combine like terms: -45 + 45 = 0 0 + x = -44.102154142 + 45 x = -44.102154142 + 45 Combine like terms: -44.102154142 + 45 = 0.897845858 x = 0.897845858 Simplifying x = 0.897845858Solution
The solution to the problem is based on the solutions from the subproblems. x = {89.102154142, 0.897845858}Solution
x = {89.102154142, 0.897845858}
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