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Simplifying 4x2 + -15x + 5 = 7x + 2 Reorder the terms: 5 + -15x + 4x2 = 7x + 2 Reorder the terms: 5 + -15x + 4x2 = 2 + 7x Solving 5 + -15x + 4x2 = 2 + 7x Solving for variable 'x'. Reorder the terms: 5 + -2 + -15x + -7x + 4x2 = 2 + 7x + -2 + -7x Combine like terms: 5 + -2 = 3 3 + -15x + -7x + 4x2 = 2 + 7x + -2 + -7x Combine like terms: -15x + -7x = -22x 3 + -22x + 4x2 = 2 + 7x + -2 + -7x Reorder the terms: 3 + -22x + 4x2 = 2 + -2 + 7x + -7x Combine like terms: 2 + -2 = 0 3 + -22x + 4x2 = 0 + 7x + -7x 3 + -22x + 4x2 = 7x + -7x Combine like terms: 7x + -7x = 0 3 + -22x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + -5.5x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -5.5x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -5.5x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -5.5x + x2 = 0 + -0.75 -5.5x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -5.5x + x2 = -0.75 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = -0.75 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = -0.75 + 7.5625 Combine like terms: -0.75 + 7.5625 = 6.8125 7.5625 + -5.5x + x2 = 6.8125 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 6.8125 Calculate the square root of the right side: 2.610076627 Break this problem into two subproblems by setting (x + -2.75) equal to 2.610076627 and -2.610076627.Subproblem 1
x + -2.75 = 2.610076627 Simplifying x + -2.75 = 2.610076627 Reorder the terms: -2.75 + x = 2.610076627 Solving -2.75 + x = 2.610076627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 2.610076627 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 2.610076627 + 2.75 x = 2.610076627 + 2.75 Combine like terms: 2.610076627 + 2.75 = 5.360076627 x = 5.360076627 Simplifying x = 5.360076627Subproblem 2
x + -2.75 = -2.610076627 Simplifying x + -2.75 = -2.610076627 Reorder the terms: -2.75 + x = -2.610076627 Solving -2.75 + x = -2.610076627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -2.610076627 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -2.610076627 + 2.75 x = -2.610076627 + 2.75 Combine like terms: -2.610076627 + 2.75 = 0.139923373 x = 0.139923373 Simplifying x = 0.139923373Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.360076627, 0.139923373}
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