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Simplifying 4x2 + -23 + 16 = -6x + 1 Reorder the terms: -23 + 16 + 4x2 = -6x + 1 Combine like terms: -23 + 16 = -7 -7 + 4x2 = -6x + 1 Reorder the terms: -7 + 4x2 = 1 + -6x Solving -7 + 4x2 = 1 + -6x Solving for variable 'x'. Reorder the terms: -7 + -1 + 6x + 4x2 = 1 + -6x + -1 + 6x Combine like terms: -7 + -1 = -8 -8 + 6x + 4x2 = 1 + -6x + -1 + 6x Reorder the terms: -8 + 6x + 4x2 = 1 + -1 + -6x + 6x Combine like terms: 1 + -1 = 0 -8 + 6x + 4x2 = 0 + -6x + 6x -8 + 6x + 4x2 = -6x + 6x Combine like terms: -6x + 6x = 0 -8 + 6x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 3x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying -4 + 3x + 2x2 = 0 Solving -4 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2 + 1.5x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 1.5x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 1.5x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 1.5x + x2 = 0 + 2 1.5x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 1.5x + x2 = 2 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 2 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 2 + 0.5625 Combine like terms: 2 + 0.5625 = 2.5625 0.5625 + 1.5x + x2 = 2.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (x + 0.75) equal to 1.600781059 and -1.600781059.Subproblem 1
x + 0.75 = 1.600781059 Simplifying x + 0.75 = 1.600781059 Reorder the terms: 0.75 + x = 1.600781059 Solving 0.75 + x = 1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 1.600781059 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 1.600781059 + -0.75 x = 1.600781059 + -0.75 Combine like terms: 1.600781059 + -0.75 = 0.850781059 x = 0.850781059 Simplifying x = 0.850781059Subproblem 2
x + 0.75 = -1.600781059 Simplifying x + 0.75 = -1.600781059 Reorder the terms: 0.75 + x = -1.600781059 Solving 0.75 + x = -1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -1.600781059 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -1.600781059 + -0.75 x = -1.600781059 + -0.75 Combine like terms: -1.600781059 + -0.75 = -2.350781059 x = -2.350781059 Simplifying x = -2.350781059Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.850781059, -2.350781059}Solution
x = {0.850781059, -2.350781059}
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