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Simplifying 4x2 + 70x + -304 = 0 Reorder the terms: -304 + 70x + 4x2 = 0 Solving -304 + 70x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-152 + 35x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-152 + 35x + 2x2)' equal to zero and attempt to solve: Simplifying -152 + 35x + 2x2 = 0 Solving -152 + 35x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -76 + 17.5x + x2 = 0 Move the constant term to the right: Add '76' to each side of the equation. -76 + 17.5x + 76 + x2 = 0 + 76 Reorder the terms: -76 + 76 + 17.5x + x2 = 0 + 76 Combine like terms: -76 + 76 = 0 0 + 17.5x + x2 = 0 + 76 17.5x + x2 = 0 + 76 Combine like terms: 0 + 76 = 76 17.5x + x2 = 76 The x term is 17.5x. Take half its coefficient (8.75). Square it (76.5625) and add it to both sides. Add '76.5625' to each side of the equation. 17.5x + 76.5625 + x2 = 76 + 76.5625 Reorder the terms: 76.5625 + 17.5x + x2 = 76 + 76.5625 Combine like terms: 76 + 76.5625 = 152.5625 76.5625 + 17.5x + x2 = 152.5625 Factor a perfect square on the left side: (x + 8.75)(x + 8.75) = 152.5625 Calculate the square root of the right side: 12.351619327 Break this problem into two subproblems by setting (x + 8.75) equal to 12.351619327 and -12.351619327.Subproblem 1
x + 8.75 = 12.351619327 Simplifying x + 8.75 = 12.351619327 Reorder the terms: 8.75 + x = 12.351619327 Solving 8.75 + x = 12.351619327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.75' to each side of the equation. 8.75 + -8.75 + x = 12.351619327 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = 12.351619327 + -8.75 x = 12.351619327 + -8.75 Combine like terms: 12.351619327 + -8.75 = 3.601619327 x = 3.601619327 Simplifying x = 3.601619327Subproblem 2
x + 8.75 = -12.351619327 Simplifying x + 8.75 = -12.351619327 Reorder the terms: 8.75 + x = -12.351619327 Solving 8.75 + x = -12.351619327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.75' to each side of the equation. 8.75 + -8.75 + x = -12.351619327 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = -12.351619327 + -8.75 x = -12.351619327 + -8.75 Combine like terms: -12.351619327 + -8.75 = -21.101619327 x = -21.101619327 Simplifying x = -21.101619327Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.601619327, -21.101619327}Solution
x = {3.601619327, -21.101619327}
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