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Simplifying 8x2 + 19x + -5 = 0 Reorder the terms: -5 + 19x + 8x2 = 0 Solving -5 + 19x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + 2.375x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + 2.375x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + 2.375x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + 2.375x + x2 = 0 + 0.625 2.375x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 2.375x + x2 = 0.625 The x term is 2.375x. Take half its coefficient (1.1875). Square it (1.41015625) and add it to both sides. Add '1.41015625' to each side of the equation. 2.375x + 1.41015625 + x2 = 0.625 + 1.41015625 Reorder the terms: 1.41015625 + 2.375x + x2 = 0.625 + 1.41015625 Combine like terms: 0.625 + 1.41015625 = 2.03515625 1.41015625 + 2.375x + x2 = 2.03515625 Factor a perfect square on the left side: (x + 1.1875)(x + 1.1875) = 2.03515625 Calculate the square root of the right side: 1.426589026 Break this problem into two subproblems by setting (x + 1.1875) equal to 1.426589026 and -1.426589026.Subproblem 1
x + 1.1875 = 1.426589026 Simplifying x + 1.1875 = 1.426589026 Reorder the terms: 1.1875 + x = 1.426589026 Solving 1.1875 + x = 1.426589026 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1875' to each side of the equation. 1.1875 + -1.1875 + x = 1.426589026 + -1.1875 Combine like terms: 1.1875 + -1.1875 = 0.0000 0.0000 + x = 1.426589026 + -1.1875 x = 1.426589026 + -1.1875 Combine like terms: 1.426589026 + -1.1875 = 0.239089026 x = 0.239089026 Simplifying x = 0.239089026Subproblem 2
x + 1.1875 = -1.426589026 Simplifying x + 1.1875 = -1.426589026 Reorder the terms: 1.1875 + x = -1.426589026 Solving 1.1875 + x = -1.426589026 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1875' to each side of the equation. 1.1875 + -1.1875 + x = -1.426589026 + -1.1875 Combine like terms: 1.1875 + -1.1875 = 0.0000 0.0000 + x = -1.426589026 + -1.1875 x = -1.426589026 + -1.1875 Combine like terms: -1.426589026 + -1.1875 = -2.614089026 x = -2.614089026 Simplifying x = -2.614089026Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.239089026, -2.614089026}
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