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Simplifying 4x2 + -3x + -30 = -12 Reorder the terms: -30 + -3x + 4x2 = -12 Solving -30 + -3x + 4x2 = -12 Solving for variable 'x'. Reorder the terms: -30 + 12 + -3x + 4x2 = -12 + 12 Combine like terms: -30 + 12 = -18 -18 + -3x + 4x2 = -12 + 12 Combine like terms: -12 + 12 = 0 -18 + -3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.5 + -0.75x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -0.75x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -0.75x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -0.75x + x2 = 0 + 4.5 -0.75x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -0.75x + x2 = 4.5 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 = 4.5 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 4.5 + 0.140625 Combine like terms: 4.5 + 0.140625 = 4.640625 0.140625 + -0.75x + x2 = 4.640625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 4.640625 Calculate the square root of the right side: 2.154210992 Break this problem into two subproblems by setting (x + -0.375) equal to 2.154210992 and -2.154210992.Subproblem 1
x + -0.375 = 2.154210992 Simplifying x + -0.375 = 2.154210992 Reorder the terms: -0.375 + x = 2.154210992 Solving -0.375 + x = 2.154210992 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 = 2.154210992 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 2.154210992 + 0.375 x = 2.154210992 + 0.375 Combine like terms: 2.154210992 + 0.375 = 2.529210992 x = 2.529210992 Simplifying x = 2.529210992Subproblem 2
x + -0.375 = -2.154210992 Simplifying x + -0.375 = -2.154210992 Reorder the terms: -0.375 + x = -2.154210992 Solving -0.375 + x = -2.154210992 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 = -2.154210992 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -2.154210992 + 0.375 x = -2.154210992 + 0.375 Combine like terms: -2.154210992 + 0.375 = -1.779210992 x = -1.779210992 Simplifying x = -1.779210992Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.529210992, -1.779210992}
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