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Simplifying 4x2 = -14x + 140 Reorder the terms: 4x2 = 140 + -14x Solving 4x2 = 140 + -14x Solving for variable 'x'. Reorder the terms: -140 + 14x + 4x2 = 140 + -14x + -140 + 14x Reorder the terms: -140 + 14x + 4x2 = 140 + -140 + -14x + 14x Combine like terms: 140 + -140 = 0 -140 + 14x + 4x2 = 0 + -14x + 14x -140 + 14x + 4x2 = -14x + 14x Combine like terms: -14x + 14x = 0 -140 + 14x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-70 + 7x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-70 + 7x + 2x2)' equal to zero and attempt to solve: Simplifying -70 + 7x + 2x2 = 0 Solving -70 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -35 + 3.5x + x2 = 0 Move the constant term to the right: Add '35' to each side of the equation. -35 + 3.5x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + 3.5x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 3.5x + x2 = 0 + 35 3.5x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 3.5x + x2 = 35 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 35 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 35 + 3.0625 Combine like terms: 35 + 3.0625 = 38.0625 3.0625 + 3.5x + x2 = 38.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 38.0625 Calculate the square root of the right side: 6.16948134 Break this problem into two subproblems by setting (x + 1.75) equal to 6.16948134 and -6.16948134.Subproblem 1
x + 1.75 = 6.16948134 Simplifying x + 1.75 = 6.16948134 Reorder the terms: 1.75 + x = 6.16948134 Solving 1.75 + x = 6.16948134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 6.16948134 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 6.16948134 + -1.75 x = 6.16948134 + -1.75 Combine like terms: 6.16948134 + -1.75 = 4.41948134 x = 4.41948134 Simplifying x = 4.41948134Subproblem 2
x + 1.75 = -6.16948134 Simplifying x + 1.75 = -6.16948134 Reorder the terms: 1.75 + x = -6.16948134 Solving 1.75 + x = -6.16948134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -6.16948134 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -6.16948134 + -1.75 x = -6.16948134 + -1.75 Combine like terms: -6.16948134 + -1.75 = -7.91948134 x = -7.91948134 Simplifying x = -7.91948134Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.41948134, -7.91948134}Solution
x = {4.41948134, -7.91948134}
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