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Simplifying 4x2 + 3x = 90 Reorder the terms: 3x + 4x2 = 90 Solving 3x + 4x2 = 90 Solving for variable 'x'. Reorder the terms: -90 + 3x + 4x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -22.5 + 0.75x + x2 = 0 Move the constant term to the right: Add '22.5' to each side of the equation. -22.5 + 0.75x + 22.5 + x2 = 0 + 22.5 Reorder the terms: -22.5 + 22.5 + 0.75x + x2 = 0 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + 0.75x + x2 = 0 + 22.5 0.75x + x2 = 0 + 22.5 Combine like terms: 0 + 22.5 = 22.5 0.75x + x2 = 22.5 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 = 22.5 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 22.5 + 0.140625 Combine like terms: 22.5 + 0.140625 = 22.640625 0.140625 + 0.75x + x2 = 22.640625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 22.640625 Calculate the square root of the right side: 4.758216578 Break this problem into two subproblems by setting (x + 0.375) equal to 4.758216578 and -4.758216578.Subproblem 1
x + 0.375 = 4.758216578 Simplifying x + 0.375 = 4.758216578 Reorder the terms: 0.375 + x = 4.758216578 Solving 0.375 + x = 4.758216578 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 = 4.758216578 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 4.758216578 + -0.375 x = 4.758216578 + -0.375 Combine like terms: 4.758216578 + -0.375 = 4.383216578 x = 4.383216578 Simplifying x = 4.383216578Subproblem 2
x + 0.375 = -4.758216578 Simplifying x + 0.375 = -4.758216578 Reorder the terms: 0.375 + x = -4.758216578 Solving 0.375 + x = -4.758216578 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 = -4.758216578 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -4.758216578 + -0.375 x = -4.758216578 + -0.375 Combine like terms: -4.758216578 + -0.375 = -5.133216578 x = -5.133216578 Simplifying x = -5.133216578Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.383216578, -5.133216578}
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