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Simplifying 5x2 + 9x + -2 = 24 Reorder the terms: -2 + 9x + 5x2 = 24 Solving -2 + 9x + 5x2 = 24 Solving for variable 'x'. Reorder the terms: -2 + -24 + 9x + 5x2 = 24 + -24 Combine like terms: -2 + -24 = -26 -26 + 9x + 5x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -26 + 9x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5.2 + 1.8x + x2 = 0 Move the constant term to the right: Add '5.2' to each side of the equation. -5.2 + 1.8x + 5.2 + x2 = 0 + 5.2 Reorder the terms: -5.2 + 5.2 + 1.8x + x2 = 0 + 5.2 Combine like terms: -5.2 + 5.2 = 0.0 0.0 + 1.8x + x2 = 0 + 5.2 1.8x + x2 = 0 + 5.2 Combine like terms: 0 + 5.2 = 5.2 1.8x + x2 = 5.2 The x term is 1.8x. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8x + 0.81 + x2 = 5.2 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = 5.2 + 0.81 Combine like terms: 5.2 + 0.81 = 6.01 0.81 + 1.8x + x2 = 6.01 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 6.01 Calculate the square root of the right side: 2.451530134 Break this problem into two subproblems by setting (x + 0.9) equal to 2.451530134 and -2.451530134.Subproblem 1
x + 0.9 = 2.451530134 Simplifying x + 0.9 = 2.451530134 Reorder the terms: 0.9 + x = 2.451530134 Solving 0.9 + x = 2.451530134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = 2.451530134 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 2.451530134 + -0.9 x = 2.451530134 + -0.9 Combine like terms: 2.451530134 + -0.9 = 1.551530134 x = 1.551530134 Simplifying x = 1.551530134Subproblem 2
x + 0.9 = -2.451530134 Simplifying x + 0.9 = -2.451530134 Reorder the terms: 0.9 + x = -2.451530134 Solving 0.9 + x = -2.451530134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = -2.451530134 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -2.451530134 + -0.9 x = -2.451530134 + -0.9 Combine like terms: -2.451530134 + -0.9 = -3.351530134 x = -3.351530134 Simplifying x = -3.351530134Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.551530134, -3.351530134}
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