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Simplifying 4x2 + 3x + -2 = 15 Reorder the terms: -2 + 3x + 4x2 = 15 Solving -2 + 3x + 4x2 = 15 Solving for variable 'x'. Reorder the terms: -2 + -15 + 3x + 4x2 = 15 + -15 Combine like terms: -2 + -15 = -17 -17 + 3x + 4x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -17 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.25 + 0.75x + x2 = 0 Move the constant term to the right: Add '4.25' to each side of the equation. -4.25 + 0.75x + 4.25 + x2 = 0 + 4.25 Reorder the terms: -4.25 + 4.25 + 0.75x + x2 = 0 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + 0.75x + x2 = 0 + 4.25 0.75x + x2 = 0 + 4.25 Combine like terms: 0 + 4.25 = 4.25 0.75x + x2 = 4.25 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 4.25 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 4.25 + 0.140625 Combine like terms: 4.25 + 0.140625 = 4.390625 0.140625 + 0.75x + x2 = 4.390625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 4.390625 Calculate the square root of the right side: 2.095381827 Break this problem into two subproblems by setting (x + 0.375) equal to 2.095381827 and -2.095381827.Subproblem 1
x + 0.375 = 2.095381827 Simplifying x + 0.375 = 2.095381827 Reorder the terms: 0.375 + x = 2.095381827 Solving 0.375 + x = 2.095381827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 2.095381827 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 2.095381827 + -0.375 x = 2.095381827 + -0.375 Combine like terms: 2.095381827 + -0.375 = 1.720381827 x = 1.720381827 Simplifying x = 1.720381827Subproblem 2
x + 0.375 = -2.095381827 Simplifying x + 0.375 = -2.095381827 Reorder the terms: 0.375 + x = -2.095381827 Solving 0.375 + x = -2.095381827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -2.095381827 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -2.095381827 + -0.375 x = -2.095381827 + -0.375 Combine like terms: -2.095381827 + -0.375 = -2.470381827 x = -2.470381827 Simplifying x = -2.470381827Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.720381827, -2.470381827}
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