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Simplifying 0 = 2x2 + 4x + -1156 Reorder the terms: 0 = -1156 + 4x + 2x2 Solving 0 = -1156 + 4x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 1156 = 1156 1156 + -4x + -2x2 = -1156 + 4x + 2x2 + 1156 + -4x + -2x2 Reorder the terms: 1156 + -4x + -2x2 = -1156 + 1156 + 4x + -4x + 2x2 + -2x2 Combine like terms: -1156 + 1156 = 0 1156 + -4x + -2x2 = 0 + 4x + -4x + 2x2 + -2x2 1156 + -4x + -2x2 = 4x + -4x + 2x2 + -2x2 Combine like terms: 4x + -4x = 0 1156 + -4x + -2x2 = 0 + 2x2 + -2x2 1156 + -4x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 1156 + -4x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(578 + -2x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(578 + -2x + -1x2)' equal to zero and attempt to solve: Simplifying 578 + -2x + -1x2 = 0 Solving 578 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -578 + 2x + x2 = 0 Move the constant term to the right: Add '578' to each side of the equation. -578 + 2x + 578 + x2 = 0 + 578 Reorder the terms: -578 + 578 + 2x + x2 = 0 + 578 Combine like terms: -578 + 578 = 0 0 + 2x + x2 = 0 + 578 2x + x2 = 0 + 578 Combine like terms: 0 + 578 = 578 2x + x2 = 578 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 578 + 1 Reorder the terms: 1 + 2x + x2 = 578 + 1 Combine like terms: 578 + 1 = 579 1 + 2x + x2 = 579 Factor a perfect square on the left side: (x + 1)(x + 1) = 579 Calculate the square root of the right side: 24.062418831 Break this problem into two subproblems by setting (x + 1) equal to 24.062418831 and -24.062418831.Subproblem 1
x + 1 = 24.062418831 Simplifying x + 1 = 24.062418831 Reorder the terms: 1 + x = 24.062418831 Solving 1 + x = 24.062418831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 24.062418831 + -1 Combine like terms: 1 + -1 = 0 0 + x = 24.062418831 + -1 x = 24.062418831 + -1 Combine like terms: 24.062418831 + -1 = 23.062418831 x = 23.062418831 Simplifying x = 23.062418831Subproblem 2
x + 1 = -24.062418831 Simplifying x + 1 = -24.062418831 Reorder the terms: 1 + x = -24.062418831 Solving 1 + x = -24.062418831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -24.062418831 + -1 Combine like terms: 1 + -1 = 0 0 + x = -24.062418831 + -1 x = -24.062418831 + -1 Combine like terms: -24.062418831 + -1 = -25.062418831 x = -25.062418831 Simplifying x = -25.062418831Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.062418831, -25.062418831}Solution
x = {23.062418831, -25.062418831}
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