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Simplifying 10x2 + 32x = 6 Reorder the terms: 32x + 10x2 = 6 Solving 32x + 10x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + 32x + 10x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 32x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 16x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 16x + 5x2)' equal to zero and attempt to solve: Simplifying -3 + 16x + 5x2 = 0 Solving -3 + 16x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + 3.2x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + 3.2x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + 3.2x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + 3.2x + x2 = 0 + 0.6 3.2x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 3.2x + x2 = 0.6 The x term is 3.2x. Take half its coefficient (1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. 3.2x + 2.56 + x2 = 0.6 + 2.56 Reorder the terms: 2.56 + 3.2x + x2 = 0.6 + 2.56 Combine like terms: 0.6 + 2.56 = 3.16 2.56 + 3.2x + x2 = 3.16 Factor a perfect square on the left side: (x + 1.6)(x + 1.6) = 3.16 Calculate the square root of the right side: 1.777638883 Break this problem into two subproblems by setting (x + 1.6) equal to 1.777638883 and -1.777638883.Subproblem 1
x + 1.6 = 1.777638883 Simplifying x + 1.6 = 1.777638883 Reorder the terms: 1.6 + x = 1.777638883 Solving 1.6 + x = 1.777638883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = 1.777638883 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = 1.777638883 + -1.6 x = 1.777638883 + -1.6 Combine like terms: 1.777638883 + -1.6 = 0.177638883 x = 0.177638883 Simplifying x = 0.177638883Subproblem 2
x + 1.6 = -1.777638883 Simplifying x + 1.6 = -1.777638883 Reorder the terms: 1.6 + x = -1.777638883 Solving 1.6 + x = -1.777638883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = -1.777638883 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = -1.777638883 + -1.6 x = -1.777638883 + -1.6 Combine like terms: -1.777638883 + -1.6 = -3.377638883 x = -3.377638883 Simplifying x = -3.377638883Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.177638883, -3.377638883}Solution
x = {0.177638883, -3.377638883}
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