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Simplifying 9x(-8x + 4) = -5 Reorder the terms: 9x(4 + -8x) = -5 (4 * 9x + -8x * 9x) = -5 (36x + -72x2) = -5 Solving 36x + -72x2 = -5 Solving for variable 'x'. Reorder the terms: 5 + 36x + -72x2 = -5 + 5 Combine like terms: -5 + 5 = 0 5 + 36x + -72x2 = 0 Begin completing the square. Divide all terms by -72 the coefficient of the squared term: Divide each side by '-72'. -0.06944444444 + -0.5x + x2 = 0 Move the constant term to the right: Add '0.06944444444' to each side of the equation. -0.06944444444 + -0.5x + 0.06944444444 + x2 = 0 + 0.06944444444 Reorder the terms: -0.06944444444 + 0.06944444444 + -0.5x + x2 = 0 + 0.06944444444 Combine like terms: -0.06944444444 + 0.06944444444 = 0.00000000000 0.00000000000 + -0.5x + x2 = 0 + 0.06944444444 -0.5x + x2 = 0 + 0.06944444444 Combine like terms: 0 + 0.06944444444 = 0.06944444444 -0.5x + x2 = 0.06944444444 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 0.06944444444 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 0.06944444444 + 0.0625 Combine like terms: 0.06944444444 + 0.0625 = 0.13194444444 0.0625 + -0.5x + x2 = 0.13194444444 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 0.13194444444 Calculate the square root of the right side: 0.363241579 Break this problem into two subproblems by setting (x + -0.25) equal to 0.363241579 and -0.363241579.Subproblem 1
x + -0.25 = 0.363241579 Simplifying x + -0.25 = 0.363241579 Reorder the terms: -0.25 + x = 0.363241579 Solving -0.25 + x = 0.363241579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 0.363241579 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.363241579 + 0.25 x = 0.363241579 + 0.25 Combine like terms: 0.363241579 + 0.25 = 0.613241579 x = 0.613241579 Simplifying x = 0.613241579Subproblem 2
x + -0.25 = -0.363241579 Simplifying x + -0.25 = -0.363241579 Reorder the terms: -0.25 + x = -0.363241579 Solving -0.25 + x = -0.363241579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -0.363241579 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.363241579 + 0.25 x = -0.363241579 + 0.25 Combine like terms: -0.363241579 + 0.25 = -0.113241579 x = -0.113241579 Simplifying x = -0.113241579Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.613241579, -0.113241579}
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