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Simplifying 8x2 + 24x + 19 = 10 + -8x Reorder the terms: 19 + 24x + 8x2 = 10 + -8x Solving 19 + 24x + 8x2 = 10 + -8x Solving for variable 'x'. Reorder the terms: 19 + -10 + 24x + 8x + 8x2 = 10 + -8x + -10 + 8x Combine like terms: 19 + -10 = 9 9 + 24x + 8x + 8x2 = 10 + -8x + -10 + 8x Combine like terms: 24x + 8x = 32x 9 + 32x + 8x2 = 10 + -8x + -10 + 8x Reorder the terms: 9 + 32x + 8x2 = 10 + -10 + -8x + 8x Combine like terms: 10 + -10 = 0 9 + 32x + 8x2 = 0 + -8x + 8x 9 + 32x + 8x2 = -8x + 8x Combine like terms: -8x + 8x = 0 9 + 32x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.125 + 4x + x2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + 4x + -1.125 + x2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + 4x + x2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + 4x + x2 = 0 + -1.125 4x + x2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 4x + x2 = -1.125 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -1.125 + 4 Reorder the terms: 4 + 4x + x2 = -1.125 + 4 Combine like terms: -1.125 + 4 = 2.875 4 + 4x + x2 = 2.875 Factor a perfect square on the left side: (x + 2)(x + 2) = 2.875 Calculate the square root of the right side: 1.695582496 Break this problem into two subproblems by setting (x + 2) equal to 1.695582496 and -1.695582496.Subproblem 1
x + 2 = 1.695582496 Simplifying x + 2 = 1.695582496 Reorder the terms: 2 + x = 1.695582496 Solving 2 + x = 1.695582496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1.695582496 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.695582496 + -2 x = 1.695582496 + -2 Combine like terms: 1.695582496 + -2 = -0.304417504 x = -0.304417504 Simplifying x = -0.304417504Subproblem 2
x + 2 = -1.695582496 Simplifying x + 2 = -1.695582496 Reorder the terms: 2 + x = -1.695582496 Solving 2 + x = -1.695582496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1.695582496 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.695582496 + -2 x = -1.695582496 + -2 Combine like terms: -1.695582496 + -2 = -3.695582496 x = -3.695582496 Simplifying x = -3.695582496Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.304417504, -3.695582496}
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