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Simplifying (3x2 + -7x + 12) + -1(2x2 + 6x + -13) = 0 Reorder the terms: (12 + -7x + 3x2) + -1(2x2 + 6x + -13) = 0 Remove parenthesis around (12 + -7x + 3x2) 12 + -7x + 3x2 + -1(2x2 + 6x + -13) = 0 Reorder the terms: 12 + -7x + 3x2 + -1(-13 + 6x + 2x2) = 0 12 + -7x + 3x2 + (-13 * -1 + 6x * -1 + 2x2 * -1) = 0 12 + -7x + 3x2 + (13 + -6x + -2x2) = 0 Reorder the terms: 12 + 13 + -7x + -6x + 3x2 + -2x2 = 0 Combine like terms: 12 + 13 = 25 25 + -7x + -6x + 3x2 + -2x2 = 0 Combine like terms: -7x + -6x = -13x 25 + -13x + 3x2 + -2x2 = 0 Combine like terms: 3x2 + -2x2 = 1x2 25 + -13x + 1x2 = 0 Solving 25 + -13x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -13x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -13x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -13x + x2 = 0 + -25 -13x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -13x + x2 = -25 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = -25 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -25 + 42.25 Combine like terms: -25 + 42.25 = 17.25 42.25 + -13x + x2 = 17.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 17.25 Calculate the square root of the right side: 4.153311931 Break this problem into two subproblems by setting (x + -6.5) equal to 4.153311931 and -4.153311931.Subproblem 1
x + -6.5 = 4.153311931 Simplifying x + -6.5 = 4.153311931 Reorder the terms: -6.5 + x = 4.153311931 Solving -6.5 + x = 4.153311931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 4.153311931 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 4.153311931 + 6.5 x = 4.153311931 + 6.5 Combine like terms: 4.153311931 + 6.5 = 10.653311931 x = 10.653311931 Simplifying x = 10.653311931Subproblem 2
x + -6.5 = -4.153311931 Simplifying x + -6.5 = -4.153311931 Reorder the terms: -6.5 + x = -4.153311931 Solving -6.5 + x = -4.153311931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -4.153311931 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -4.153311931 + 6.5 x = -4.153311931 + 6.5 Combine like terms: -4.153311931 + 6.5 = 2.346688069 x = 2.346688069 Simplifying x = 2.346688069Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.653311931, 2.346688069}
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