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Simplifying 10x2 + -6x + -288 = 0 Reorder the terms: -288 + -6x + 10x2 = 0 Solving -288 + -6x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-144 + -3x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-144 + -3x + 5x2)' equal to zero and attempt to solve: Simplifying -144 + -3x + 5x2 = 0 Solving -144 + -3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -28.8 + -0.6x + x2 = 0 Move the constant term to the right: Add '28.8' to each side of the equation. -28.8 + -0.6x + 28.8 + x2 = 0 + 28.8 Reorder the terms: -28.8 + 28.8 + -0.6x + x2 = 0 + 28.8 Combine like terms: -28.8 + 28.8 = 0.0 0.0 + -0.6x + x2 = 0 + 28.8 -0.6x + x2 = 0 + 28.8 Combine like terms: 0 + 28.8 = 28.8 -0.6x + x2 = 28.8 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 28.8 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 28.8 + 0.09 Combine like terms: 28.8 + 0.09 = 28.89 0.09 + -0.6x + x2 = 28.89 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 28.89 Calculate the square root of the right side: 5.37494186 Break this problem into two subproblems by setting (x + -0.3) equal to 5.37494186 and -5.37494186.Subproblem 1
x + -0.3 = 5.37494186 Simplifying x + -0.3 = 5.37494186 Reorder the terms: -0.3 + x = 5.37494186 Solving -0.3 + x = 5.37494186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 5.37494186 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 5.37494186 + 0.3 x = 5.37494186 + 0.3 Combine like terms: 5.37494186 + 0.3 = 5.67494186 x = 5.67494186 Simplifying x = 5.67494186Subproblem 2
x + -0.3 = -5.37494186 Simplifying x + -0.3 = -5.37494186 Reorder the terms: -0.3 + x = -5.37494186 Solving -0.3 + x = -5.37494186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -5.37494186 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -5.37494186 + 0.3 x = -5.37494186 + 0.3 Combine like terms: -5.37494186 + 0.3 = -5.07494186 x = -5.07494186 Simplifying x = -5.07494186Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.67494186, -5.07494186}Solution
x = {5.67494186, -5.07494186}
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