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Simplifying x(4x + -3) = 30 Reorder the terms: x(-3 + 4x) = 30 (-3 * x + 4x * x) = 30 (-3x + 4x2) = 30 Solving -3x + 4x2 = 30 Solving for variable 'x'. Reorder the terms: -30 + -3x + 4x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + -3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -7.5 + -0.75x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -0.75x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -0.75x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -0.75x + x2 = 0 + 7.5 -0.75x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -0.75x + x2 = 7.5 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 7.5 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 7.5 + 0.140625 Combine like terms: 7.5 + 0.140625 = 7.640625 0.140625 + -0.75x + x2 = 7.640625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 7.640625 Calculate the square root of the right side: 2.764168048 Break this problem into two subproblems by setting (x + -0.375) equal to 2.764168048 and -2.764168048.Subproblem 1
x + -0.375 = 2.764168048 Simplifying x + -0.375 = 2.764168048 Reorder the terms: -0.375 + x = 2.764168048 Solving -0.375 + x = 2.764168048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 2.764168048 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 2.764168048 + 0.375 x = 2.764168048 + 0.375 Combine like terms: 2.764168048 + 0.375 = 3.139168048 x = 3.139168048 Simplifying x = 3.139168048Subproblem 2
x + -0.375 = -2.764168048 Simplifying x + -0.375 = -2.764168048 Reorder the terms: -0.375 + x = -2.764168048 Solving -0.375 + x = -2.764168048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -2.764168048 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -2.764168048 + 0.375 x = -2.764168048 + 0.375 Combine like terms: -2.764168048 + 0.375 = -2.389168048 x = -2.389168048 Simplifying x = -2.389168048Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.139168048, -2.389168048}
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