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Simplifying 0.30(480) + 0.55x = (0.40x)(x + 480) Multiply 0.30 * 480 144 + 0.55x = (0.40x)(x + 480) Remove parenthesis around (0.40x) 144 + 0.55x = 0.40x(x + 480) Reorder the terms: 144 + 0.55x = 0.40x(480 + x) 144 + 0.55x = (480 * 0.40x + x * 0.40x) 144 + 0.55x = (192x + 0.40x2) Solving 144 + 0.55x = 192x + 0.40x2 Solving for variable 'x'. Combine like terms: 0.55x + -192x = -191.45x 144 + -191.45x + -0.40x2 = 192x + 0.40x2 + -192x + -0.40x2 Reorder the terms: 144 + -191.45x + -0.40x2 = 192x + -192x + 0.40x2 + -0.40x2 Combine like terms: 192x + -192x = 0 144 + -191.45x + -0.40x2 = 0 + 0.40x2 + -0.40x2 144 + -191.45x + -0.40x2 = 0.40x2 + -0.40x2 Combine like terms: 0.40x2 + -0.40x2 = 0.00 144 + -191.45x + -0.40x2 = 0.00 Begin completing the square. Divide all terms by -0.40 the coefficient of the squared term: Divide each side by '-0.40'. -360 + 478.625x + x2 = 0 Move the constant term to the right: Add '360' to each side of the equation. -360 + 478.625x + 360 + x2 = 0 + 360 Reorder the terms: -360 + 360 + 478.625x + x2 = 0 + 360 Combine like terms: -360 + 360 = 0 0 + 478.625x + x2 = 0 + 360 478.625x + x2 = 0 + 360 Combine like terms: 0 + 360 = 360 478.625x + x2 = 360 The x term is 478.625x. Take half its coefficient (239.3125). Square it (57270.47266) and add it to both sides. Add '57270.47266' to each side of the equation. 478.625x + 57270.47266 + x2 = 360 + 57270.47266 Reorder the terms: 57270.47266 + 478.625x + x2 = 360 + 57270.47266 Combine like terms: 360 + 57270.47266 = 57630.47266 57270.47266 + 478.625x + x2 = 57630.47266 Factor a perfect square on the left side: (x + 239.3125)(x + 239.3125) = 57630.47266 Calculate the square root of the right side: 240.063476314 Break this problem into two subproblems by setting (x + 239.3125) equal to 240.063476314 and -240.063476314.Subproblem 1
x + 239.3125 = 240.063476314 Simplifying x + 239.3125 = 240.063476314 Reorder the terms: 239.3125 + x = 240.063476314 Solving 239.3125 + x = 240.063476314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-239.3125' to each side of the equation. 239.3125 + -239.3125 + x = 240.063476314 + -239.3125 Combine like terms: 239.3125 + -239.3125 = 0.0000 0.0000 + x = 240.063476314 + -239.3125 x = 240.063476314 + -239.3125 Combine like terms: 240.063476314 + -239.3125 = 0.750976314 x = 0.750976314 Simplifying x = 0.750976314Subproblem 2
x + 239.3125 = -240.063476314 Simplifying x + 239.3125 = -240.063476314 Reorder the terms: 239.3125 + x = -240.063476314 Solving 239.3125 + x = -240.063476314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-239.3125' to each side of the equation. 239.3125 + -239.3125 + x = -240.063476314 + -239.3125 Combine like terms: 239.3125 + -239.3125 = 0.0000 0.0000 + x = -240.063476314 + -239.3125 x = -240.063476314 + -239.3125 Combine like terms: -240.063476314 + -239.3125 = -479.375976314 x = -479.375976314 Simplifying x = -479.375976314Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.750976314, -479.375976314}
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