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Simplifying 4x2 + 3x + -1 = 13 Reorder the terms: -1 + 3x + 4x2 = 13 Solving -1 + 3x + 4x2 = 13 Solving for variable 'x'. Reorder the terms: -1 + -13 + 3x + 4x2 = 13 + -13 Combine like terms: -1 + -13 = -14 -14 + 3x + 4x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -14 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.5 + 0.75x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 0.75x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 0.75x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 0.75x + x2 = 0 + 3.5 0.75x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 0.75x + x2 = 3.5 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 = 3.5 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 3.5 + 0.140625 Combine like terms: 3.5 + 0.140625 = 3.640625 0.140625 + 0.75x + x2 = 3.640625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 3.640625 Calculate the square root of the right side: 1.90804219 Break this problem into two subproblems by setting (x + 0.375) equal to 1.90804219 and -1.90804219.Subproblem 1
x + 0.375 = 1.90804219 Simplifying x + 0.375 = 1.90804219 Reorder the terms: 0.375 + x = 1.90804219 Solving 0.375 + x = 1.90804219 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 = 1.90804219 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 1.90804219 + -0.375 x = 1.90804219 + -0.375 Combine like terms: 1.90804219 + -0.375 = 1.53304219 x = 1.53304219 Simplifying x = 1.53304219Subproblem 2
x + 0.375 = -1.90804219 Simplifying x + 0.375 = -1.90804219 Reorder the terms: 0.375 + x = -1.90804219 Solving 0.375 + x = -1.90804219 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 = -1.90804219 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -1.90804219 + -0.375 x = -1.90804219 + -0.375 Combine like terms: -1.90804219 + -0.375 = -2.28304219 x = -2.28304219 Simplifying x = -2.28304219Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.53304219, -2.28304219}
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