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Simplifying 5 + -10x(x + -7) = -5(1 + 4x) Reorder the terms: 5 + -10x(-7 + x) = -5(1 + 4x) 5 + (-7 * -10x + x * -10x) = -5(1 + 4x) 5 + (70x + -10x2) = -5(1 + 4x) 5 + 70x + -10x2 = (1 * -5 + 4x * -5) 5 + 70x + -10x2 = (-5 + -20x) Solving 5 + 70x + -10x2 = -5 + -20x Solving for variable 'x'. Reorder the terms: 5 + 5 + 70x + 20x + -10x2 = -5 + -20x + 5 + 20x Combine like terms: 5 + 5 = 10 10 + 70x + 20x + -10x2 = -5 + -20x + 5 + 20x Combine like terms: 70x + 20x = 90x 10 + 90x + -10x2 = -5 + -20x + 5 + 20x Reorder the terms: 10 + 90x + -10x2 = -5 + 5 + -20x + 20x Combine like terms: -5 + 5 = 0 10 + 90x + -10x2 = 0 + -20x + 20x 10 + 90x + -10x2 = -20x + 20x Combine like terms: -20x + 20x = 0 10 + 90x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(1 + 9x + -1x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(1 + 9x + -1x2)' equal to zero and attempt to solve: Simplifying 1 + 9x + -1x2 = 0 Solving 1 + 9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + -9x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -9x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -9x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -9x + x2 = 0 + 1 -9x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -9x + x2 = 1 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 = 1 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 1 + 20.25 Combine like terms: 1 + 20.25 = 21.25 20.25 + -9x + x2 = 21.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (x + -4.5) equal to 4.609772229 and -4.609772229.Subproblem 1
x + -4.5 = 4.609772229 Simplifying x + -4.5 = 4.609772229 Reorder the terms: -4.5 + x = 4.609772229 Solving -4.5 + x = 4.609772229 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 = 4.609772229 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 4.609772229 + 4.5 x = 4.609772229 + 4.5 Combine like terms: 4.609772229 + 4.5 = 9.109772229 x = 9.109772229 Simplifying x = 9.109772229Subproblem 2
x + -4.5 = -4.609772229 Simplifying x + -4.5 = -4.609772229 Reorder the terms: -4.5 + x = -4.609772229 Solving -4.5 + x = -4.609772229 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 = -4.609772229 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -4.609772229 + 4.5 x = -4.609772229 + 4.5 Combine like terms: -4.609772229 + 4.5 = -0.109772229 x = -0.109772229 Simplifying x = -0.109772229Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.109772229, -0.109772229}Solution
x = {9.109772229, -0.109772229}
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