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Simplifying 20x2 = 9 + 13x Solving 20x2 = 9 + 13x Solving for variable 'x'. Reorder the terms: -9 + -13x + 20x2 = 9 + 13x + -9 + -13x Reorder the terms: -9 + -13x + 20x2 = 9 + -9 + 13x + -13x Combine like terms: 9 + -9 = 0 -9 + -13x + 20x2 = 0 + 13x + -13x -9 + -13x + 20x2 = 13x + -13x Combine like terms: 13x + -13x = 0 -9 + -13x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.45 + -0.65x + x2 = 0 Move the constant term to the right: Add '0.45' to each side of the equation. -0.45 + -0.65x + 0.45 + x2 = 0 + 0.45 Reorder the terms: -0.45 + 0.45 + -0.65x + x2 = 0 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + -0.65x + x2 = 0 + 0.45 -0.65x + x2 = 0 + 0.45 Combine like terms: 0 + 0.45 = 0.45 -0.65x + x2 = 0.45 The x term is -0.65x. Take half its coefficient (-0.325). Square it (0.105625) and add it to both sides. Add '0.105625' to each side of the equation. -0.65x + 0.105625 + x2 = 0.45 + 0.105625 Reorder the terms: 0.105625 + -0.65x + x2 = 0.45 + 0.105625 Combine like terms: 0.45 + 0.105625 = 0.555625 0.105625 + -0.65x + x2 = 0.555625 Factor a perfect square on the left side: (x + -0.325)(x + -0.325) = 0.555625 Calculate the square root of the right side: 0.745402576 Break this problem into two subproblems by setting (x + -0.325) equal to 0.745402576 and -0.745402576.Subproblem 1
x + -0.325 = 0.745402576 Simplifying x + -0.325 = 0.745402576 Reorder the terms: -0.325 + x = 0.745402576 Solving -0.325 + x = 0.745402576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.325' to each side of the equation. -0.325 + 0.325 + x = 0.745402576 + 0.325 Combine like terms: -0.325 + 0.325 = 0.000 0.000 + x = 0.745402576 + 0.325 x = 0.745402576 + 0.325 Combine like terms: 0.745402576 + 0.325 = 1.070402576 x = 1.070402576 Simplifying x = 1.070402576Subproblem 2
x + -0.325 = -0.745402576 Simplifying x + -0.325 = -0.745402576 Reorder the terms: -0.325 + x = -0.745402576 Solving -0.325 + x = -0.745402576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.325' to each side of the equation. -0.325 + 0.325 + x = -0.745402576 + 0.325 Combine like terms: -0.325 + 0.325 = 0.000 0.000 + x = -0.745402576 + 0.325 x = -0.745402576 + 0.325 Combine like terms: -0.745402576 + 0.325 = -0.420402576 x = -0.420402576 Simplifying x = -0.420402576Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.070402576, -0.420402576}
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