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Simplifying 0.4x + 0.25x(75 + -1x) = 30 0.4x + (75 * 0.25x + -1x * 0.25x) = 30 0.4x + (18.75x + -0.25x2) = 30 Combine like terms: 0.4x + 18.75x = 19.15x 19.15x + -0.25x2 = 30 Solving 19.15x + -0.25x2 = 30 Solving for variable 'x'. Reorder the terms: -30 + 19.15x + -0.25x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + 19.15x + -0.25x2 = 0 Begin completing the square. Divide all terms by -0.25 the coefficient of the squared term: Divide each side by '-0.25'. 120 + -76.6x + x2 = 0 Move the constant term to the right: Add '-120' to each side of the equation. 120 + -76.6x + -120 + x2 = 0 + -120 Reorder the terms: 120 + -120 + -76.6x + x2 = 0 + -120 Combine like terms: 120 + -120 = 0 0 + -76.6x + x2 = 0 + -120 -76.6x + x2 = 0 + -120 Combine like terms: 0 + -120 = -120 -76.6x + x2 = -120 The x term is -76.6x. Take half its coefficient (-38.3). Square it (1466.89) and add it to both sides. Add '1466.89' to each side of the equation. -76.6x + 1466.89 + x2 = -120 + 1466.89 Reorder the terms: 1466.89 + -76.6x + x2 = -120 + 1466.89 Combine like terms: -120 + 1466.89 = 1346.89 1466.89 + -76.6x + x2 = 1346.89 Factor a perfect square on the left side: (x + -38.3)(x + -38.3) = 1346.89 Calculate the square root of the right side: 36.7 Break this problem into two subproblems by setting (x + -38.3) equal to 36.7 and -36.7.Subproblem 1
x + -38.3 = 36.7 Simplifying x + -38.3 = 36.7 Reorder the terms: -38.3 + x = 36.7 Solving -38.3 + x = 36.7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '38.3' to each side of the equation. -38.3 + 38.3 + x = 36.7 + 38.3 Combine like terms: -38.3 + 38.3 = 0.0 0.0 + x = 36.7 + 38.3 x = 36.7 + 38.3 Combine like terms: 36.7 + 38.3 = 75 x = 75 Simplifying x = 75Subproblem 2
x + -38.3 = -36.7 Simplifying x + -38.3 = -36.7 Reorder the terms: -38.3 + x = -36.7 Solving -38.3 + x = -36.7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '38.3' to each side of the equation. -38.3 + 38.3 + x = -36.7 + 38.3 Combine like terms: -38.3 + 38.3 = 0.0 0.0 + x = -36.7 + 38.3 x = -36.7 + 38.3 Combine like terms: -36.7 + 38.3 = 1.6 x = 1.6 Simplifying x = 1.6Solution
The solution to the problem is based on the solutions from the subproblems. x = {75, 1.6}
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