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Simplifying 32x = -30x2 + 2 Reorder the terms: 32x = 2 + -30x2 Solving 32x = 2 + -30x2 Solving for variable 'x'. Reorder the terms: -2 + 32x + 30x2 = 2 + -30x2 + -2 + 30x2 Reorder the terms: -2 + 32x + 30x2 = 2 + -2 + -30x2 + 30x2 Combine like terms: 2 + -2 = 0 -2 + 32x + 30x2 = 0 + -30x2 + 30x2 -2 + 32x + 30x2 = -30x2 + 30x2 Combine like terms: -30x2 + 30x2 = 0 -2 + 32x + 30x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 16x + 15x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 16x + 15x2)' equal to zero and attempt to solve: Simplifying -1 + 16x + 15x2 = 0 Solving -1 + 16x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.06666666667 + 1.066666667x + x2 = 0 Move the constant term to the right: Add '0.06666666667' to each side of the equation. -0.06666666667 + 1.066666667x + 0.06666666667 + x2 = 0 + 0.06666666667 Reorder the terms: -0.06666666667 + 0.06666666667 + 1.066666667x + x2 = 0 + 0.06666666667 Combine like terms: -0.06666666667 + 0.06666666667 = 0.00000000000 0.00000000000 + 1.066666667x + x2 = 0 + 0.06666666667 1.066666667x + x2 = 0 + 0.06666666667 Combine like terms: 0 + 0.06666666667 = 0.06666666667 1.066666667x + x2 = 0.06666666667 The x term is 1.066666667x. Take half its coefficient (0.5333333335). Square it (0.2844444446) and add it to both sides. Add '0.2844444446' to each side of the equation. 1.066666667x + 0.2844444446 + x2 = 0.06666666667 + 0.2844444446 Reorder the terms: 0.2844444446 + 1.066666667x + x2 = 0.06666666667 + 0.2844444446 Combine like terms: 0.06666666667 + 0.2844444446 = 0.35111111127 0.2844444446 + 1.066666667x + x2 = 0.35111111127 Factor a perfect square on the left side: (x + 0.5333333335)(x + 0.5333333335) = 0.35111111127 Calculate the square root of the right side: 0.592546295 Break this problem into two subproblems by setting (x + 0.5333333335) equal to 0.592546295 and -0.592546295.Subproblem 1
x + 0.5333333335 = 0.592546295 Simplifying x + 0.5333333335 = 0.592546295 Reorder the terms: 0.5333333335 + x = 0.592546295 Solving 0.5333333335 + x = 0.592546295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5333333335' to each side of the equation. 0.5333333335 + -0.5333333335 + x = 0.592546295 + -0.5333333335 Combine like terms: 0.5333333335 + -0.5333333335 = 0.0000000000 0.0000000000 + x = 0.592546295 + -0.5333333335 x = 0.592546295 + -0.5333333335 Combine like terms: 0.592546295 + -0.5333333335 = 0.0592129615 x = 0.0592129615 Simplifying x = 0.0592129615Subproblem 2
x + 0.5333333335 = -0.592546295 Simplifying x + 0.5333333335 = -0.592546295 Reorder the terms: 0.5333333335 + x = -0.592546295 Solving 0.5333333335 + x = -0.592546295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5333333335' to each side of the equation. 0.5333333335 + -0.5333333335 + x = -0.592546295 + -0.5333333335 Combine like terms: 0.5333333335 + -0.5333333335 = 0.0000000000 0.0000000000 + x = -0.592546295 + -0.5333333335 x = -0.592546295 + -0.5333333335 Combine like terms: -0.592546295 + -0.5333333335 = -1.1258796285 x = -1.1258796285 Simplifying x = -1.1258796285Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0592129615, -1.1258796285}Solution
x = {0.0592129615, -1.1258796285}
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