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Simplifying 6x2 + 6x + -72 = 3 Reorder the terms: -72 + 6x + 6x2 = 3 Solving -72 + 6x + 6x2 = 3 Solving for variable 'x'. Reorder the terms: -72 + -3 + 6x + 6x2 = 3 + -3 Combine like terms: -72 + -3 = -75 -75 + 6x + 6x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -75 + 6x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-25 + 2x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-25 + 2x + 2x2)' equal to zero and attempt to solve: Simplifying -25 + 2x + 2x2 = 0 Solving -25 + 2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12.5 + x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x + x2 = 0 + 12.5 x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 x + x2 = 12.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 12.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 12.5 + 0.25 Combine like terms: 12.5 + 0.25 = 12.75 1.25 + x2 = 12.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 12.75 Calculate the square root of the right side: 3.570714214 Break this problem into two subproblems by setting (x + 0.5) equal to 3.570714214 and -3.570714214.Subproblem 1
x + 0.5 = 3.570714214 Simplifying x + 0.5 = 3.570714214 Reorder the terms: 0.5 + x = 3.570714214 Solving 0.5 + x = 3.570714214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 3.570714214 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.570714214 + -0.5 x = 3.570714214 + -0.5 Combine like terms: 3.570714214 + -0.5 = 3.070714214 x = 3.070714214 Simplifying x = 3.070714214Subproblem 2
x + 0.5 = -3.570714214 Simplifying x + 0.5 = -3.570714214 Reorder the terms: 0.5 + x = -3.570714214 Solving 0.5 + x = -3.570714214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -3.570714214 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.570714214 + -0.5 x = -3.570714214 + -0.5 Combine like terms: -3.570714214 + -0.5 = -4.070714214 x = -4.070714214 Simplifying x = -4.070714214Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.070714214, -4.070714214}Solution
x = {3.070714214, -4.070714214}
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