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Simplifying 0 = 5x * x + 32x + 11 Multiply x * x 0 = 5x2 + 32x + 11 Reorder the terms: 0 = 11 + 32x + 5x2 Solving 0 = 11 + 32x + 5x2 Solving for variable 'x'. Combine like terms: 0 + -11 = -11 -11 + -32x + -5x2 = 11 + 32x + 5x2 + -11 + -32x + -5x2 Reorder the terms: -11 + -32x + -5x2 = 11 + -11 + 32x + -32x + 5x2 + -5x2 Combine like terms: 11 + -11 = 0 -11 + -32x + -5x2 = 0 + 32x + -32x + 5x2 + -5x2 -11 + -32x + -5x2 = 32x + -32x + 5x2 + -5x2 Combine like terms: 32x + -32x = 0 -11 + -32x + -5x2 = 0 + 5x2 + -5x2 -11 + -32x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -11 + -32x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(11 + 32x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(11 + 32x + 5x2)' equal to zero and attempt to solve: Simplifying 11 + 32x + 5x2 = 0 Solving 11 + 32x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.2 + 6.4x + x2 = 0 Move the constant term to the right: Add '-2.2' to each side of the equation. 2.2 + 6.4x + -2.2 + x2 = 0 + -2.2 Reorder the terms: 2.2 + -2.2 + 6.4x + x2 = 0 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + 6.4x + x2 = 0 + -2.2 6.4x + x2 = 0 + -2.2 Combine like terms: 0 + -2.2 = -2.2 6.4x + x2 = -2.2 The x term is 6.4x. Take half its coefficient (3.2). Square it (10.24) and add it to both sides. Add '10.24' to each side of the equation. 6.4x + 10.24 + x2 = -2.2 + 10.24 Reorder the terms: 10.24 + 6.4x + x2 = -2.2 + 10.24 Combine like terms: -2.2 + 10.24 = 8.04 10.24 + 6.4x + x2 = 8.04 Factor a perfect square on the left side: (x + 3.2)(x + 3.2) = 8.04 Calculate the square root of the right side: 2.835489376 Break this problem into two subproblems by setting (x + 3.2) equal to 2.835489376 and -2.835489376.Subproblem 1
x + 3.2 = 2.835489376 Simplifying x + 3.2 = 2.835489376 Reorder the terms: 3.2 + x = 2.835489376 Solving 3.2 + x = 2.835489376 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.2' to each side of the equation. 3.2 + -3.2 + x = 2.835489376 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + x = 2.835489376 + -3.2 x = 2.835489376 + -3.2 Combine like terms: 2.835489376 + -3.2 = -0.364510624 x = -0.364510624 Simplifying x = -0.364510624Subproblem 2
x + 3.2 = -2.835489376 Simplifying x + 3.2 = -2.835489376 Reorder the terms: 3.2 + x = -2.835489376 Solving 3.2 + x = -2.835489376 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.2' to each side of the equation. 3.2 + -3.2 + x = -2.835489376 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + x = -2.835489376 + -3.2 x = -2.835489376 + -3.2 Combine like terms: -2.835489376 + -3.2 = -6.035489376 x = -6.035489376 Simplifying x = -6.035489376Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.364510624, -6.035489376}Solution
x = {-0.364510624, -6.035489376}
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