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Simplifying 8x2 + 23x + -20 = 0 Reorder the terms: -20 + 23x + 8x2 = 0 Solving -20 + 23x + 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'. -2.5 + 2.875x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 2.875x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 2.875x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 2.875x + x2 = 0 + 2.5 2.875x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 2.875x + x2 = 2.5 The x term is 2.875x. Take half its coefficient (1.4375). Square it (2.06640625) and add it to both sides. Add '2.06640625' to each side of the equation. 2.875x + 2.06640625 + x2 = 2.5 + 2.06640625 Reorder the terms: 2.06640625 + 2.875x + x2 = 2.5 + 2.06640625 Combine like terms: 2.5 + 2.06640625 = 4.56640625 2.06640625 + 2.875x + x2 = 4.56640625 Factor a perfect square on the left side: (x + 1.4375)(x + 1.4375) = 4.56640625 Calculate the square root of the right side: 2.136915125 Break this problem into two subproblems by setting (x + 1.4375) equal to 2.136915125 and -2.136915125.Subproblem 1
x + 1.4375 = 2.136915125 Simplifying x + 1.4375 = 2.136915125 Reorder the terms: 1.4375 + x = 2.136915125 Solving 1.4375 + x = 2.136915125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4375' to each side of the equation. 1.4375 + -1.4375 + x = 2.136915125 + -1.4375 Combine like terms: 1.4375 + -1.4375 = 0.0000 0.0000 + x = 2.136915125 + -1.4375 x = 2.136915125 + -1.4375 Combine like terms: 2.136915125 + -1.4375 = 0.699415125 x = 0.699415125 Simplifying x = 0.699415125Subproblem 2
x + 1.4375 = -2.136915125 Simplifying x + 1.4375 = -2.136915125 Reorder the terms: 1.4375 + x = -2.136915125 Solving 1.4375 + x = -2.136915125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4375' to each side of the equation. 1.4375 + -1.4375 + x = -2.136915125 + -1.4375 Combine like terms: 1.4375 + -1.4375 = 0.0000 0.0000 + x = -2.136915125 + -1.4375 x = -2.136915125 + -1.4375 Combine like terms: -2.136915125 + -1.4375 = -3.574415125 x = -3.574415125 Simplifying x = -3.574415125Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.699415125, -3.574415125}
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