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Simplifying 10x + 20x2 = 100x2 + -20 + -3x Reorder the terms: 10x + 20x2 = -20 + -3x + 100x2 Solving 10x + 20x2 = -20 + -3x + 100x2 Solving for variable 'x'. Reorder the terms: 20 + 10x + 3x + 20x2 + -100x2 = -20 + -3x + 100x2 + 20 + 3x + -100x2 Combine like terms: 10x + 3x = 13x 20 + 13x + 20x2 + -100x2 = -20 + -3x + 100x2 + 20 + 3x + -100x2 Combine like terms: 20x2 + -100x2 = -80x2 20 + 13x + -80x2 = -20 + -3x + 100x2 + 20 + 3x + -100x2 Reorder the terms: 20 + 13x + -80x2 = -20 + 20 + -3x + 3x + 100x2 + -100x2 Combine like terms: -20 + 20 = 0 20 + 13x + -80x2 = 0 + -3x + 3x + 100x2 + -100x2 20 + 13x + -80x2 = -3x + 3x + 100x2 + -100x2 Combine like terms: -3x + 3x = 0 20 + 13x + -80x2 = 0 + 100x2 + -100x2 20 + 13x + -80x2 = 100x2 + -100x2 Combine like terms: 100x2 + -100x2 = 0 20 + 13x + -80x2 = 0 Begin completing the square. Divide all terms by -80 the coefficient of the squared term: Divide each side by '-80'. -0.25 + -0.1625x + x2 = 0.0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -0.1625x + 0.25 + x2 = 0.0 + 0.25 Reorder the terms: -0.25 + 0.25 + -0.1625x + x2 = 0.0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -0.1625x + x2 = 0.0 + 0.25 -0.1625x + x2 = 0.0 + 0.25 Combine like terms: 0.0 + 0.25 = 0.25 -0.1625x + x2 = 0.25 The x term is -0.1625x. Take half its coefficient (-0.08125). Square it (0.0066015625) and add it to both sides. Add '0.0066015625' to each side of the equation. -0.1625x + 0.0066015625 + x2 = 0.25 + 0.0066015625 Reorder the terms: 0.0066015625 + -0.1625x + x2 = 0.25 + 0.0066015625 Combine like terms: 0.25 + 0.0066015625 = 0.2566015625 0.0066015625 + -0.1625x + x2 = 0.2566015625 Factor a perfect square on the left side: (x + -0.08125)(x + -0.08125) = 0.2566015625 Calculate the square root of the right side: 0.506558548 Break this problem into two subproblems by setting (x + -0.08125) equal to 0.506558548 and -0.506558548.Subproblem 1
x + -0.08125 = 0.506558548 Simplifying x + -0.08125 = 0.506558548 Reorder the terms: -0.08125 + x = 0.506558548 Solving -0.08125 + x = 0.506558548 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08125' to each side of the equation. -0.08125 + 0.08125 + x = 0.506558548 + 0.08125 Combine like terms: -0.08125 + 0.08125 = 0.00000 0.00000 + x = 0.506558548 + 0.08125 x = 0.506558548 + 0.08125 Combine like terms: 0.506558548 + 0.08125 = 0.587808548 x = 0.587808548 Simplifying x = 0.587808548Subproblem 2
x + -0.08125 = -0.506558548 Simplifying x + -0.08125 = -0.506558548 Reorder the terms: -0.08125 + x = -0.506558548 Solving -0.08125 + x = -0.506558548 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08125' to each side of the equation. -0.08125 + 0.08125 + x = -0.506558548 + 0.08125 Combine like terms: -0.08125 + 0.08125 = 0.00000 0.00000 + x = -0.506558548 + 0.08125 x = -0.506558548 + 0.08125 Combine like terms: -0.506558548 + 0.08125 = -0.425308548 x = -0.425308548 Simplifying x = -0.425308548Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.587808548, -0.425308548}
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