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Simplifying -5x2 + 9x + 19 = 0 Reorder the terms: 19 + 9x + -5x2 = 0 Solving 19 + 9x + -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'. -3.8 + -1.8x + x2 = 0 Move the constant term to the right: Add '3.8' to each side of the equation. -3.8 + -1.8x + 3.8 + x2 = 0 + 3.8 Reorder the terms: -3.8 + 3.8 + -1.8x + x2 = 0 + 3.8 Combine like terms: -3.8 + 3.8 = 0.0 0.0 + -1.8x + x2 = 0 + 3.8 -1.8x + x2 = 0 + 3.8 Combine like terms: 0 + 3.8 = 3.8 -1.8x + x2 = 3.8 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 = 3.8 + 0.81 Reorder the terms: 0.81 + -1.8x + x2 = 3.8 + 0.81 Combine like terms: 3.8 + 0.81 = 4.61 0.81 + -1.8x + x2 = 4.61 Factor a perfect square on the left side: (x + -0.9)(x + -0.9) = 4.61 Calculate the square root of the right side: 2.147091055 Break this problem into two subproblems by setting (x + -0.9) equal to 2.147091055 and -2.147091055.Subproblem 1
x + -0.9 = 2.147091055 Simplifying x + -0.9 = 2.147091055 Reorder the terms: -0.9 + x = 2.147091055 Solving -0.9 + x = 2.147091055 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 = 2.147091055 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = 2.147091055 + 0.9 x = 2.147091055 + 0.9 Combine like terms: 2.147091055 + 0.9 = 3.047091055 x = 3.047091055 Simplifying x = 3.047091055Subproblem 2
x + -0.9 = -2.147091055 Simplifying x + -0.9 = -2.147091055 Reorder the terms: -0.9 + x = -2.147091055 Solving -0.9 + x = -2.147091055 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 = -2.147091055 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = -2.147091055 + 0.9 x = -2.147091055 + 0.9 Combine like terms: -2.147091055 + 0.9 = -1.247091055 x = -1.247091055 Simplifying x = -1.247091055Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.047091055, -1.247091055}
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