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Simplifying -10 + 6x2 + 36x = 0 Reorder the terms: -10 + 36x + 6x2 = 0 Solving -10 + 36x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 18x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 18x + 3x2)' equal to zero and attempt to solve: Simplifying -5 + 18x + 3x2 = 0 Solving -5 + 18x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.666666667 + 6x + x2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + 6x + 1.666666667 + x2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + 6x + x2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + 6x + x2 = 0 + 1.666666667 6x + x2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 6x + x2 = 1.666666667 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 1.666666667 + 9 Reorder the terms: 9 + 6x + x2 = 1.666666667 + 9 Combine like terms: 1.666666667 + 9 = 10.666666667 9 + 6x + x2 = 10.666666667 Factor a perfect square on the left side: (x + 3)(x + 3) = 10.666666667 Calculate the square root of the right side: 3.265986324 Break this problem into two subproblems by setting (x + 3) equal to 3.265986324 and -3.265986324.Subproblem 1
x + 3 = 3.265986324 Simplifying x + 3 = 3.265986324 Reorder the terms: 3 + x = 3.265986324 Solving 3 + x = 3.265986324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.265986324 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.265986324 + -3 x = 3.265986324 + -3 Combine like terms: 3.265986324 + -3 = 0.265986324 x = 0.265986324 Simplifying x = 0.265986324Subproblem 2
x + 3 = -3.265986324 Simplifying x + 3 = -3.265986324 Reorder the terms: 3 + x = -3.265986324 Solving 3 + x = -3.265986324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.265986324 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.265986324 + -3 x = -3.265986324 + -3 Combine like terms: -3.265986324 + -3 = -6.265986324 x = -6.265986324 Simplifying x = -6.265986324Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.265986324, -6.265986324}Solution
x = {0.265986324, -6.265986324}
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