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Simplifying 2.4x2 + 1.2x = 36 Reorder the terms: 1.2x + 2.4x2 = 36 Solving 1.2x + 2.4x2 = 36 Solving for variable 'x'. Reorder the terms: -36 + 1.2x + 2.4x2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + 1.2x + 2.4x2 = 0 Begin completing the square. Divide all terms by 2.4 the coefficient of the squared term: Divide each side by '2.4'. -15 + 0.5x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 0.5x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 0.5x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 0.5x + x2 = 0 + 15 0.5x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 0.5x + x2 = 15 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 15 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 15 + 0.0625 Combine like terms: 15 + 0.0625 = 15.0625 0.0625 + 0.5x + x2 = 15.0625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 15.0625 Calculate the square root of the right side: 3.881043674 Break this problem into two subproblems by setting (x + 0.25) equal to 3.881043674 and -3.881043674.Subproblem 1
x + 0.25 = 3.881043674 Simplifying x + 0.25 = 3.881043674 Reorder the terms: 0.25 + x = 3.881043674 Solving 0.25 + x = 3.881043674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 3.881043674 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 3.881043674 + -0.25 x = 3.881043674 + -0.25 Combine like terms: 3.881043674 + -0.25 = 3.631043674 x = 3.631043674 Simplifying x = 3.631043674Subproblem 2
x + 0.25 = -3.881043674 Simplifying x + 0.25 = -3.881043674 Reorder the terms: 0.25 + x = -3.881043674 Solving 0.25 + x = -3.881043674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -3.881043674 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -3.881043674 + -0.25 x = -3.881043674 + -0.25 Combine like terms: -3.881043674 + -0.25 = -4.131043674 x = -4.131043674 Simplifying x = -4.131043674Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.631043674, -4.131043674}
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