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Simplifying (6x2 + -2x + -35) + (9x2 + 5x) = 0 Reorder the terms: (-35 + -2x + 6x2) + (9x2 + 5x) = 0 Remove parenthesis around (-35 + -2x + 6x2) -35 + -2x + 6x2 + (9x2 + 5x) = 0 Reorder the terms: -35 + -2x + 6x2 + (5x + 9x2) = 0 Remove parenthesis around (5x + 9x2) -35 + -2x + 6x2 + 5x + 9x2 = 0 Reorder the terms: -35 + -2x + 5x + 6x2 + 9x2 = 0 Combine like terms: -2x + 5x = 3x -35 + 3x + 6x2 + 9x2 = 0 Combine like terms: 6x2 + 9x2 = 15x2 -35 + 3x + 15x2 = 0 Solving -35 + 3x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -2.333333333 + 0.2x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + 0.2x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + 0.2x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + 0.2x + x2 = 0 + 2.333333333 0.2x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 0.2x + x2 = 2.333333333 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = 2.333333333 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 2.333333333 + 0.01 Combine like terms: 2.333333333 + 0.01 = 2.343333333 0.01 + 0.2x + x2 = 2.343333333 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 2.343333333 Calculate the square root of the right side: 1.530795 Break this problem into two subproblems by setting (x + 0.1) equal to 1.530795 and -1.530795.Subproblem 1
x + 0.1 = 1.530795 Simplifying x + 0.1 = 1.530795 Reorder the terms: 0.1 + x = 1.530795 Solving 0.1 + x = 1.530795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 1.530795 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 1.530795 + -0.1 x = 1.530795 + -0.1 Combine like terms: 1.530795 + -0.1 = 1.430795 x = 1.430795 Simplifying x = 1.430795Subproblem 2
x + 0.1 = -1.530795 Simplifying x + 0.1 = -1.530795 Reorder the terms: 0.1 + x = -1.530795 Solving 0.1 + x = -1.530795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -1.530795 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -1.530795 + -0.1 x = -1.530795 + -0.1 Combine like terms: -1.530795 + -0.1 = -1.630795 x = -1.630795 Simplifying x = -1.630795Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.430795, -1.630795}
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