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Simplifying 0 = -4x2 + 24x + -23 Reorder the terms: 0 = -23 + 24x + -4x2 Solving 0 = -23 + 24x + -4x2 Solving for variable 'x'. Combine like terms: 0 + 23 = 23 23 + -24x + 4x2 = -23 + 24x + -4x2 + 23 + -24x + 4x2 Reorder the terms: 23 + -24x + 4x2 = -23 + 23 + 24x + -24x + -4x2 + 4x2 Combine like terms: -23 + 23 = 0 23 + -24x + 4x2 = 0 + 24x + -24x + -4x2 + 4x2 23 + -24x + 4x2 = 24x + -24x + -4x2 + 4x2 Combine like terms: 24x + -24x = 0 23 + -24x + 4x2 = 0 + -4x2 + 4x2 23 + -24x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 23 + -24x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 5.75 + -6x + x2 = 0 Move the constant term to the right: Add '-5.75' to each side of the equation. 5.75 + -6x + -5.75 + x2 = 0 + -5.75 Reorder the terms: 5.75 + -5.75 + -6x + x2 = 0 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + -6x + x2 = 0 + -5.75 -6x + x2 = 0 + -5.75 Combine like terms: 0 + -5.75 = -5.75 -6x + x2 = -5.75 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -5.75 + 9 Reorder the terms: 9 + -6x + x2 = -5.75 + 9 Combine like terms: -5.75 + 9 = 3.25 9 + -6x + x2 = 3.25 Factor a perfect square on the left side: (x + -3)(x + -3) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (x + -3) equal to 1.802775638 and -1.802775638.Subproblem 1
x + -3 = 1.802775638 Simplifying x + -3 = 1.802775638 Reorder the terms: -3 + x = 1.802775638 Solving -3 + x = 1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 1.802775638 + 3 Combine like terms: -3 + 3 = 0 0 + x = 1.802775638 + 3 x = 1.802775638 + 3 Combine like terms: 1.802775638 + 3 = 4.802775638 x = 4.802775638 Simplifying x = 4.802775638Subproblem 2
x + -3 = -1.802775638 Simplifying x + -3 = -1.802775638 Reorder the terms: -3 + x = -1.802775638 Solving -3 + x = -1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -1.802775638 + 3 Combine like terms: -3 + 3 = 0 0 + x = -1.802775638 + 3 x = -1.802775638 + 3 Combine like terms: -1.802775638 + 3 = 1.197224362 x = 1.197224362 Simplifying x = 1.197224362Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.802775638, 1.197224362}
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