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Simplifying 2x * x + 6x = 75 Multiply x * x 2x2 + 6x = 75 Reorder the terms: 6x + 2x2 = 75 Solving 6x + 2x2 = 75 Solving for variable 'x'. Reorder the terms: -75 + 6x + 2x2 = 75 + -75 Combine like terms: 75 + -75 = 0 -75 + 6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -37.5 + 3x + x2 = 0 Move the constant term to the right: Add '37.5' to each side of the equation. -37.5 + 3x + 37.5 + x2 = 0 + 37.5 Reorder the terms: -37.5 + 37.5 + 3x + x2 = 0 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + 3x + x2 = 0 + 37.5 3x + x2 = 0 + 37.5 Combine like terms: 0 + 37.5 = 37.5 3x + x2 = 37.5 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 37.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 37.5 + 2.25 Combine like terms: 37.5 + 2.25 = 39.75 2.25 + 3x + x2 = 39.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 39.75 Calculate the square root of the right side: 6.304760106 Break this problem into two subproblems by setting (x + 1.5) equal to 6.304760106 and -6.304760106.Subproblem 1
x + 1.5 = 6.304760106 Simplifying x + 1.5 = 6.304760106 Reorder the terms: 1.5 + x = 6.304760106 Solving 1.5 + x = 6.304760106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 6.304760106 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 6.304760106 + -1.5 x = 6.304760106 + -1.5 Combine like terms: 6.304760106 + -1.5 = 4.804760106 x = 4.804760106 Simplifying x = 4.804760106Subproblem 2
x + 1.5 = -6.304760106 Simplifying x + 1.5 = -6.304760106 Reorder the terms: 1.5 + x = -6.304760106 Solving 1.5 + x = -6.304760106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -6.304760106 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -6.304760106 + -1.5 x = -6.304760106 + -1.5 Combine like terms: -6.304760106 + -1.5 = -7.804760106 x = -7.804760106 Simplifying x = -7.804760106Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.804760106, -7.804760106}
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