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Simplifying 10x(4 + x) = 12 (4 * 10x + x * 10x) = 12 (40x + 10x2) = 12 Solving 40x + 10x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + 40x + 10x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 40x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 20x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 20x + 5x2)' equal to zero and attempt to solve: Simplifying -6 + 20x + 5x2 = 0 Solving -6 + 20x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.2 + 4x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 4x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 4x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 4x + x2 = 0 + 1.2 4x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 4x + x2 = 1.2 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 1.2 + 4 Reorder the terms: 4 + 4x + x2 = 1.2 + 4 Combine like terms: 1.2 + 4 = 5.2 4 + 4x + x2 = 5.2 Factor a perfect square on the left side: (x + 2)(x + 2) = 5.2 Calculate the square root of the right side: 2.28035085 Break this problem into two subproblems by setting (x + 2) equal to 2.28035085 and -2.28035085.Subproblem 1
x + 2 = 2.28035085 Simplifying x + 2 = 2.28035085 Reorder the terms: 2 + x = 2.28035085 Solving 2 + x = 2.28035085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.28035085 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.28035085 + -2 x = 2.28035085 + -2 Combine like terms: 2.28035085 + -2 = 0.28035085 x = 0.28035085 Simplifying x = 0.28035085Subproblem 2
x + 2 = -2.28035085 Simplifying x + 2 = -2.28035085 Reorder the terms: 2 + x = -2.28035085 Solving 2 + x = -2.28035085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.28035085 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.28035085 + -2 x = -2.28035085 + -2 Combine like terms: -2.28035085 + -2 = -4.28035085 x = -4.28035085 Simplifying x = -4.28035085Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.28035085, -4.28035085}Solution
x = {0.28035085, -4.28035085}
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