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Simplifying 10x2 + -36x = -12 Reorder the terms: -36x + 10x2 = -12 Solving -36x + 10x2 = -12 Solving for variable 'x'. Reorder the terms: 12 + -36x + 10x2 = -12 + 12 Combine like terms: -12 + 12 = 0 12 + -36x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -18x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + -18x + 5x2)' equal to zero and attempt to solve: Simplifying 6 + -18x + 5x2 = 0 Solving 6 + -18x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.2 + -3.6x + x2 = 0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + -3.6x + -1.2 + x2 = 0 + -1.2 Reorder the terms: 1.2 + -1.2 + -3.6x + x2 = 0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + -3.6x + x2 = 0 + -1.2 -3.6x + x2 = 0 + -1.2 Combine like terms: 0 + -1.2 = -1.2 -3.6x + x2 = -1.2 The x term is -3.6x. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6x + 3.24 + x2 = -1.2 + 3.24 Reorder the terms: 3.24 + -3.6x + x2 = -1.2 + 3.24 Combine like terms: -1.2 + 3.24 = 2.04 3.24 + -3.6x + x2 = 2.04 Factor a perfect square on the left side: (x + -1.8)(x + -1.8) = 2.04 Calculate the square root of the right side: 1.428285686 Break this problem into two subproblems by setting (x + -1.8) equal to 1.428285686 and -1.428285686.Subproblem 1
x + -1.8 = 1.428285686 Simplifying x + -1.8 = 1.428285686 Reorder the terms: -1.8 + x = 1.428285686 Solving -1.8 + x = 1.428285686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = 1.428285686 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = 1.428285686 + 1.8 x = 1.428285686 + 1.8 Combine like terms: 1.428285686 + 1.8 = 3.228285686 x = 3.228285686 Simplifying x = 3.228285686Subproblem 2
x + -1.8 = -1.428285686 Simplifying x + -1.8 = -1.428285686 Reorder the terms: -1.8 + x = -1.428285686 Solving -1.8 + x = -1.428285686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = -1.428285686 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = -1.428285686 + 1.8 x = -1.428285686 + 1.8 Combine like terms: -1.428285686 + 1.8 = 0.371714314 x = 0.371714314 Simplifying x = 0.371714314Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.228285686, 0.371714314}Solution
x = {3.228285686, 0.371714314}
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