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Simplifying -24x2 + -56x = 23 Reorder the terms: -56x + -24x2 = 23 Solving -56x + -24x2 = 23 Solving for variable 'x'. Reorder the terms: -23 + -56x + -24x2 = 23 + -23 Combine like terms: 23 + -23 = 0 -23 + -56x + -24x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(23 + 56x + 24x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(23 + 56x + 24x2)' equal to zero and attempt to solve: Simplifying 23 + 56x + 24x2 = 0 Solving 23 + 56x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. 0.9583333333 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '-0.9583333333' to each side of the equation. 0.9583333333 + 2.333333333x + -0.9583333333 + x2 = 0 + -0.9583333333 Reorder the terms: 0.9583333333 + -0.9583333333 + 2.333333333x + x2 = 0 + -0.9583333333 Combine like terms: 0.9583333333 + -0.9583333333 = 0.0000000000 0.0000000000 + 2.333333333x + x2 = 0 + -0.9583333333 2.333333333x + x2 = 0 + -0.9583333333 Combine like terms: 0 + -0.9583333333 = -0.9583333333 2.333333333x + x2 = -0.9583333333 The x term is 2.333333333x. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333x + 1.361111112 + x2 = -0.9583333333 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = -0.9583333333 + 1.361111112 Combine like terms: -0.9583333333 + 1.361111112 = 0.4027777787 1.361111112 + 2.333333333x + x2 = 0.4027777787 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 0.4027777787 Calculate the square root of the right side: 0.63464776 Break this problem into two subproblems by setting (x + 1.166666667) equal to 0.63464776 and -0.63464776.Subproblem 1
x + 1.166666667 = 0.63464776 Simplifying x + 1.166666667 = 0.63464776 Reorder the terms: 1.166666667 + x = 0.63464776 Solving 1.166666667 + x = 0.63464776 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = 0.63464776 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 0.63464776 + -1.166666667 x = 0.63464776 + -1.166666667 Combine like terms: 0.63464776 + -1.166666667 = -0.532018907 x = -0.532018907 Simplifying x = -0.532018907Subproblem 2
x + 1.166666667 = -0.63464776 Simplifying x + 1.166666667 = -0.63464776 Reorder the terms: 1.166666667 + x = -0.63464776 Solving 1.166666667 + x = -0.63464776 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = -0.63464776 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -0.63464776 + -1.166666667 x = -0.63464776 + -1.166666667 Combine like terms: -0.63464776 + -1.166666667 = -1.801314427 x = -1.801314427 Simplifying x = -1.801314427Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.532018907, -1.801314427}Solution
x = {-0.532018907, -1.801314427}
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