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Simplifying -13x2 + 3x + -7x2 + 6 = 0 Reorder the terms: 6 + 3x + -13x2 + -7x2 = 0 Combine like terms: -13x2 + -7x2 = -20x2 6 + 3x + -20x2 = 0 Solving 6 + 3x + -20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -20 the coefficient of the squared term: Divide each side by '-20'. -0.3 + -0.15x + x2 = 0.0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + -0.15x + 0.3 + x2 = 0.0 + 0.3 Reorder the terms: -0.3 + 0.3 + -0.15x + x2 = 0.0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + -0.15x + x2 = 0.0 + 0.3 -0.15x + x2 = 0.0 + 0.3 Combine like terms: 0.0 + 0.3 = 0.3 -0.15x + x2 = 0.3 The x term is -0.15x. Take half its coefficient (-0.075). Square it (0.005625) and add it to both sides. Add '0.005625' to each side of the equation. -0.15x + 0.005625 + x2 = 0.3 + 0.005625 Reorder the terms: 0.005625 + -0.15x + x2 = 0.3 + 0.005625 Combine like terms: 0.3 + 0.005625 = 0.305625 0.005625 + -0.15x + x2 = 0.305625 Factor a perfect square on the left side: (x + -0.075)(x + -0.075) = 0.305625 Calculate the square root of the right side: 0.55283361 Break this problem into two subproblems by setting (x + -0.075) equal to 0.55283361 and -0.55283361.Subproblem 1
x + -0.075 = 0.55283361 Simplifying x + -0.075 = 0.55283361 Reorder the terms: -0.075 + x = 0.55283361 Solving -0.075 + x = 0.55283361 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.075' to each side of the equation. -0.075 + 0.075 + x = 0.55283361 + 0.075 Combine like terms: -0.075 + 0.075 = 0.000 0.000 + x = 0.55283361 + 0.075 x = 0.55283361 + 0.075 Combine like terms: 0.55283361 + 0.075 = 0.62783361 x = 0.62783361 Simplifying x = 0.62783361Subproblem 2
x + -0.075 = -0.55283361 Simplifying x + -0.075 = -0.55283361 Reorder the terms: -0.075 + x = -0.55283361 Solving -0.075 + x = -0.55283361 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.075' to each side of the equation. -0.075 + 0.075 + x = -0.55283361 + 0.075 Combine like terms: -0.075 + 0.075 = 0.000 0.000 + x = -0.55283361 + 0.075 x = -0.55283361 + 0.075 Combine like terms: -0.55283361 + 0.075 = -0.47783361 x = -0.47783361 Simplifying x = -0.47783361Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.62783361, -0.47783361}
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