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Simplifying 7y2(5x2 + 43x + -30) = 0 Reorder the terms: 7y2(-30 + 43x + 5x2) = 0 (-30 * 7y2 + 43x * 7y2 + 5x2 * 7y2) = 0 Reorder the terms: (301xy2 + 35x2y2 + -210y2) = 0 (301xy2 + 35x2y2 + -210y2) = 0 Solving 301xy2 + 35x2y2 + -210y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7y2'. 7y2(43x + 5x2 + -30) = 0 Ignore the factor 7.Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve: Simplifying y2 = 0 Solving y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y2' to each side of the equation. y2 + -1y2 = 0 + -1y2 Remove the zero: 0 = -1y2 Simplifying 0 = -1y2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(43x + 5x2 + -30)' equal to zero and attempt to solve: Simplifying 43x + 5x2 + -30 = 0 Reorder the terms: -30 + 43x + 5x2 = 0 Solving -30 + 43x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -6 + 8.6x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 8.6x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 8.6x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 8.6x + x2 = 0 + 6 8.6x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 8.6x + x2 = 6 The x term is 8.6x. Take half its coefficient (4.3). Square it (18.49) and add it to both sides. Add '18.49' to each side of the equation. 8.6x + 18.49 + x2 = 6 + 18.49 Reorder the terms: 18.49 + 8.6x + x2 = 6 + 18.49 Combine like terms: 6 + 18.49 = 24.49 18.49 + 8.6x + x2 = 24.49 Factor a perfect square on the left side: (x + 4.3)(x + 4.3) = 24.49 Calculate the square root of the right side: 4.948737213 Break this problem into two subproblems by setting (x + 4.3) equal to 4.948737213 and -4.948737213.Subproblem 1
x + 4.3 = 4.948737213 Simplifying x + 4.3 = 4.948737213 Reorder the terms: 4.3 + x = 4.948737213 Solving 4.3 + x = 4.948737213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.3' to each side of the equation. 4.3 + -4.3 + x = 4.948737213 + -4.3 Combine like terms: 4.3 + -4.3 = 0.0 0.0 + x = 4.948737213 + -4.3 x = 4.948737213 + -4.3 Combine like terms: 4.948737213 + -4.3 = 0.648737213 x = 0.648737213 Simplifying x = 0.648737213Subproblem 2
x + 4.3 = -4.948737213 Simplifying x + 4.3 = -4.948737213 Reorder the terms: 4.3 + x = -4.948737213 Solving 4.3 + x = -4.948737213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.3' to each side of the equation. 4.3 + -4.3 + x = -4.948737213 + -4.3 Combine like terms: 4.3 + -4.3 = 0.0 0.0 + x = -4.948737213 + -4.3 x = -4.948737213 + -4.3 Combine like terms: -4.948737213 + -4.3 = -9.248737213 x = -9.248737213 Simplifying x = -9.248737213Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.648737213, -9.248737213}Solution
x = {0.648737213, -9.248737213}
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