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Simplifying 8x(2x + 1.3) = 4x + 8.7 Reorder the terms: 8x(1.3 + 2x) = 4x + 8.7 (1.3 * 8x + 2x * 8x) = 4x + 8.7 (10.4x + 16x2) = 4x + 8.7 Reorder the terms: 10.4x + 16x2 = 8.7 + 4x Solving 10.4x + 16x2 = 8.7 + 4x Solving for variable 'x'. Reorder the terms: -8.7 + 10.4x + -4x + 16x2 = 8.7 + 4x + -8.7 + -4x Combine like terms: 10.4x + -4x = 6.4x -8.7 + 6.4x + 16x2 = 8.7 + 4x + -8.7 + -4x Reorder the terms: -8.7 + 6.4x + 16x2 = 8.7 + -8.7 + 4x + -4x Combine like terms: 8.7 + -8.7 = 0.0 -8.7 + 6.4x + 16x2 = 0.0 + 4x + -4x -8.7 + 6.4x + 16x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -8.7 + 6.4x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.54375 + 0.4x + x2 = 0 Move the constant term to the right: Add '0.54375' to each side of the equation. -0.54375 + 0.4x + 0.54375 + x2 = 0 + 0.54375 Reorder the terms: -0.54375 + 0.54375 + 0.4x + x2 = 0 + 0.54375 Combine like terms: -0.54375 + 0.54375 = 0.00000 0.00000 + 0.4x + x2 = 0 + 0.54375 0.4x + x2 = 0 + 0.54375 Combine like terms: 0 + 0.54375 = 0.54375 0.4x + x2 = 0.54375 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 0.54375 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 0.54375 + 0.04 Combine like terms: 0.54375 + 0.04 = 0.58375 0.04 + 0.4x + x2 = 0.58375 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 0.58375 Calculate the square root of the right side: 0.764035339 Break this problem into two subproblems by setting (x + 0.2) equal to 0.764035339 and -0.764035339.Subproblem 1
x + 0.2 = 0.764035339 Simplifying x + 0.2 = 0.764035339 Reorder the terms: 0.2 + x = 0.764035339 Solving 0.2 + x = 0.764035339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 0.764035339 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 0.764035339 + -0.2 x = 0.764035339 + -0.2 Combine like terms: 0.764035339 + -0.2 = 0.564035339 x = 0.564035339 Simplifying x = 0.564035339Subproblem 2
x + 0.2 = -0.764035339 Simplifying x + 0.2 = -0.764035339 Reorder the terms: 0.2 + x = -0.764035339 Solving 0.2 + x = -0.764035339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -0.764035339 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -0.764035339 + -0.2 x = -0.764035339 + -0.2 Combine like terms: -0.764035339 + -0.2 = -0.964035339 x = -0.964035339 Simplifying x = -0.964035339Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.564035339, -0.964035339}
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