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Simplifying 0 = 24x2 + -24x + -7 Reorder the terms: 0 = -7 + -24x + 24x2 Solving 0 = -7 + -24x + 24x2 Solving for variable 'x'. Combine like terms: 0 + 7 = 7 7 + 24x + -24x2 = -7 + -24x + 24x2 + 7 + 24x + -24x2 Reorder the terms: 7 + 24x + -24x2 = -7 + 7 + -24x + 24x + 24x2 + -24x2 Combine like terms: -7 + 7 = 0 7 + 24x + -24x2 = 0 + -24x + 24x + 24x2 + -24x2 7 + 24x + -24x2 = -24x + 24x + 24x2 + -24x2 Combine like terms: -24x + 24x = 0 7 + 24x + -24x2 = 0 + 24x2 + -24x2 7 + 24x + -24x2 = 24x2 + -24x2 Combine like terms: 24x2 + -24x2 = 0 7 + 24x + -24x2 = 0 Begin completing the square. Divide all terms by -24 the coefficient of the squared term: Divide each side by '-24'. -0.2916666667 + -1x + x2 = 0 Move the constant term to the right: Add '0.2916666667' to each side of the equation. -0.2916666667 + -1x + 0.2916666667 + x2 = 0 + 0.2916666667 Reorder the terms: -0.2916666667 + 0.2916666667 + -1x + x2 = 0 + 0.2916666667 Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000 0.0000000000 + -1x + x2 = 0 + 0.2916666667 -1x + x2 = 0 + 0.2916666667 Combine like terms: 0 + 0.2916666667 = 0.2916666667 -1x + x2 = 0.2916666667 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.2916666667 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.2916666667 + 0.25 Combine like terms: 0.2916666667 + 0.25 = 0.5416666667 0.25 + -1x + x2 = 0.5416666667 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.5416666667 Calculate the square root of the right side: 0.735980072 Break this problem into two subproblems by setting (x + -0.5) equal to 0.735980072 and -0.735980072.Subproblem 1
x + -0.5 = 0.735980072 Simplifying x + -0.5 = 0.735980072 Reorder the terms: -0.5 + x = 0.735980072 Solving -0.5 + x = 0.735980072 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.735980072 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.735980072 + 0.5 x = 0.735980072 + 0.5 Combine like terms: 0.735980072 + 0.5 = 1.235980072 x = 1.235980072 Simplifying x = 1.235980072Subproblem 2
x + -0.5 = -0.735980072 Simplifying x + -0.5 = -0.735980072 Reorder the terms: -0.5 + x = -0.735980072 Solving -0.5 + x = -0.735980072 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.735980072 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.735980072 + 0.5 x = -0.735980072 + 0.5 Combine like terms: -0.735980072 + 0.5 = -0.235980072 x = -0.235980072 Simplifying x = -0.235980072Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.235980072, -0.235980072}
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