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Simplifying 5x2 + -24x + 18 = 0 Reorder the terms: 18 + -24x + 5x2 = 0 Solving 18 + -24x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3.6 + -4.8x + x2 = 0 Move the constant term to the right: Add '-3.6' to each side of the equation. 3.6 + -4.8x + -3.6 + x2 = 0 + -3.6 Reorder the terms: 3.6 + -3.6 + -4.8x + x2 = 0 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + -4.8x + x2 = 0 + -3.6 -4.8x + x2 = 0 + -3.6 Combine like terms: 0 + -3.6 = -3.6 -4.8x + x2 = -3.6 The x term is -4.8x. Take half its coefficient (-2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. -4.8x + 5.76 + x2 = -3.6 + 5.76 Reorder the terms: 5.76 + -4.8x + x2 = -3.6 + 5.76 Combine like terms: -3.6 + 5.76 = 2.16 5.76 + -4.8x + x2 = 2.16 Factor a perfect square on the left side: (x + -2.4)(x + -2.4) = 2.16 Calculate the square root of the right side: 1.469693846 Break this problem into two subproblems by setting (x + -2.4) equal to 1.469693846 and -1.469693846.Subproblem 1
x + -2.4 = 1.469693846 Simplifying x + -2.4 = 1.469693846 Reorder the terms: -2.4 + x = 1.469693846 Solving -2.4 + x = 1.469693846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + x = 1.469693846 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x = 1.469693846 + 2.4 x = 1.469693846 + 2.4 Combine like terms: 1.469693846 + 2.4 = 3.869693846 x = 3.869693846 Simplifying x = 3.869693846Subproblem 2
x + -2.4 = -1.469693846 Simplifying x + -2.4 = -1.469693846 Reorder the terms: -2.4 + x = -1.469693846 Solving -2.4 + x = -1.469693846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + x = -1.469693846 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x = -1.469693846 + 2.4 x = -1.469693846 + 2.4 Combine like terms: -1.469693846 + 2.4 = 0.930306154 x = 0.930306154 Simplifying x = 0.930306154Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.869693846, 0.930306154}
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