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Simplifying (12x2 + 3x + -9) + (13x2 + -5x + -3) = 0 Reorder the terms: (-9 + 3x + 12x2) + (13x2 + -5x + -3) = 0 Remove parenthesis around (-9 + 3x + 12x2) -9 + 3x + 12x2 + (13x2 + -5x + -3) = 0 Reorder the terms: -9 + 3x + 12x2 + (-3 + -5x + 13x2) = 0 Remove parenthesis around (-3 + -5x + 13x2) -9 + 3x + 12x2 + -3 + -5x + 13x2 = 0 Reorder the terms: -9 + -3 + 3x + -5x + 12x2 + 13x2 = 0 Combine like terms: -9 + -3 = -12 -12 + 3x + -5x + 12x2 + 13x2 = 0 Combine like terms: 3x + -5x = -2x -12 + -2x + 12x2 + 13x2 = 0 Combine like terms: 12x2 + 13x2 = 25x2 -12 + -2x + 25x2 = 0 Solving -12 + -2x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.48 + -0.08x + x2 = 0 Move the constant term to the right: Add '0.48' to each side of the equation. -0.48 + -0.08x + 0.48 + x2 = 0 + 0.48 Reorder the terms: -0.48 + 0.48 + -0.08x + x2 = 0 + 0.48 Combine like terms: -0.48 + 0.48 = 0.00 0.00 + -0.08x + x2 = 0 + 0.48 -0.08x + x2 = 0 + 0.48 Combine like terms: 0 + 0.48 = 0.48 -0.08x + x2 = 0.48 The x term is -0.08x. Take half its coefficient (-0.04). Square it (0.0016) and add it to both sides. Add '0.0016' to each side of the equation. -0.08x + 0.0016 + x2 = 0.48 + 0.0016 Reorder the terms: 0.0016 + -0.08x + x2 = 0.48 + 0.0016 Combine like terms: 0.48 + 0.0016 = 0.4816 0.0016 + -0.08x + x2 = 0.4816 Factor a perfect square on the left side: (x + -0.04)(x + -0.04) = 0.4816 Calculate the square root of the right side: 0.693974063 Break this problem into two subproblems by setting (x + -0.04) equal to 0.693974063 and -0.693974063.Subproblem 1
x + -0.04 = 0.693974063 Simplifying x + -0.04 = 0.693974063 Reorder the terms: -0.04 + x = 0.693974063 Solving -0.04 + x = 0.693974063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04' to each side of the equation. -0.04 + 0.04 + x = 0.693974063 + 0.04 Combine like terms: -0.04 + 0.04 = 0.00 0.00 + x = 0.693974063 + 0.04 x = 0.693974063 + 0.04 Combine like terms: 0.693974063 + 0.04 = 0.733974063 x = 0.733974063 Simplifying x = 0.733974063Subproblem 2
x + -0.04 = -0.693974063 Simplifying x + -0.04 = -0.693974063 Reorder the terms: -0.04 + x = -0.693974063 Solving -0.04 + x = -0.693974063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04' to each side of the equation. -0.04 + 0.04 + x = -0.693974063 + 0.04 Combine like terms: -0.04 + 0.04 = 0.00 0.00 + x = -0.693974063 + 0.04 x = -0.693974063 + 0.04 Combine like terms: -0.693974063 + 0.04 = -0.653974063 x = -0.653974063 Simplifying x = -0.653974063Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.733974063, -0.653974063}
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