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Simplifying 10x2 + 48x + -32 = 0 Reorder the terms: -32 + 48x + 10x2 = 0 Solving -32 + 48x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-16 + 24x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-16 + 24x + 5x2)' equal to zero and attempt to solve: Simplifying -16 + 24x + 5x2 = 0 Solving -16 + 24x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.2 + 4.8x + x2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + 4.8x + 3.2 + x2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + 4.8x + x2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + 4.8x + x2 = 0 + 3.2 4.8x + x2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 4.8x + x2 = 3.2 The x term is 4.8x. Take half its coefficient (2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. 4.8x + 5.76 + x2 = 3.2 + 5.76 Reorder the terms: 5.76 + 4.8x + x2 = 3.2 + 5.76 Combine like terms: 3.2 + 5.76 = 8.96 5.76 + 4.8x + x2 = 8.96 Factor a perfect square on the left side: (x + 2.4)(x + 2.4) = 8.96 Calculate the square root of the right side: 2.993325909 Break this problem into two subproblems by setting (x + 2.4) equal to 2.993325909 and -2.993325909.Subproblem 1
x + 2.4 = 2.993325909 Simplifying x + 2.4 = 2.993325909 Reorder the terms: 2.4 + x = 2.993325909 Solving 2.4 + x = 2.993325909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + x = 2.993325909 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x = 2.993325909 + -2.4 x = 2.993325909 + -2.4 Combine like terms: 2.993325909 + -2.4 = 0.593325909 x = 0.593325909 Simplifying x = 0.593325909Subproblem 2
x + 2.4 = -2.993325909 Simplifying x + 2.4 = -2.993325909 Reorder the terms: 2.4 + x = -2.993325909 Solving 2.4 + x = -2.993325909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + x = -2.993325909 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x = -2.993325909 + -2.4 x = -2.993325909 + -2.4 Combine like terms: -2.993325909 + -2.4 = -5.393325909 x = -5.393325909 Simplifying x = -5.393325909Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.593325909, -5.393325909}Solution
x = {0.593325909, -5.393325909}
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