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Simplifying 30x2 + 65x + -35 = 0 Reorder the terms: -35 + 65x + 30x2 = 0 Solving -35 + 65x + 30x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-7 + 13x + 6x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-7 + 13x + 6x2)' equal to zero and attempt to solve: Simplifying -7 + 13x + 6x2 = 0 Solving -7 + 13x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.166666667 + 2.166666667x + x2 = 0 Move the constant term to the right: Add '1.166666667' to each side of the equation. -1.166666667 + 2.166666667x + 1.166666667 + x2 = 0 + 1.166666667 Reorder the terms: -1.166666667 + 1.166666667 + 2.166666667x + x2 = 0 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + 2.166666667x + x2 = 0 + 1.166666667 2.166666667x + x2 = 0 + 1.166666667 Combine like terms: 0 + 1.166666667 = 1.166666667 2.166666667x + x2 = 1.166666667 The x term is 2.166666667x. Take half its coefficient (1.083333334). Square it (1.173611113) and add it to both sides. Add '1.173611113' to each side of the equation. 2.166666667x + 1.173611113 + x2 = 1.166666667 + 1.173611113 Reorder the terms: 1.173611113 + 2.166666667x + x2 = 1.166666667 + 1.173611113 Combine like terms: 1.166666667 + 1.173611113 = 2.34027778 1.173611113 + 2.166666667x + x2 = 2.34027778 Factor a perfect square on the left side: (x + 1.083333334)(x + 1.083333334) = 2.34027778 Calculate the square root of the right side: 1.529796647 Break this problem into two subproblems by setting (x + 1.083333334) equal to 1.529796647 and -1.529796647.Subproblem 1
x + 1.083333334 = 1.529796647 Simplifying x + 1.083333334 = 1.529796647 Reorder the terms: 1.083333334 + x = 1.529796647 Solving 1.083333334 + x = 1.529796647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.083333334' to each side of the equation. 1.083333334 + -1.083333334 + x = 1.529796647 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + x = 1.529796647 + -1.083333334 x = 1.529796647 + -1.083333334 Combine like terms: 1.529796647 + -1.083333334 = 0.446463313 x = 0.446463313 Simplifying x = 0.446463313Subproblem 2
x + 1.083333334 = -1.529796647 Simplifying x + 1.083333334 = -1.529796647 Reorder the terms: 1.083333334 + x = -1.529796647 Solving 1.083333334 + x = -1.529796647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.083333334' to each side of the equation. 1.083333334 + -1.083333334 + x = -1.529796647 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + x = -1.529796647 + -1.083333334 x = -1.529796647 + -1.083333334 Combine like terms: -1.529796647 + -1.083333334 = -2.613129981 x = -2.613129981 Simplifying x = -2.613129981Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.446463313, -2.613129981}Solution
x = {0.446463313, -2.613129981}
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