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Simplifying (2x2 + -7x + 10) + (3x2 + 9x + -68) = 0 Reorder the terms: (10 + -7x + 2x2) + (3x2 + 9x + -68) = 0 Remove parenthesis around (10 + -7x + 2x2) 10 + -7x + 2x2 + (3x2 + 9x + -68) = 0 Reorder the terms: 10 + -7x + 2x2 + (-68 + 9x + 3x2) = 0 Remove parenthesis around (-68 + 9x + 3x2) 10 + -7x + 2x2 + -68 + 9x + 3x2 = 0 Reorder the terms: 10 + -68 + -7x + 9x + 2x2 + 3x2 = 0 Combine like terms: 10 + -68 = -58 -58 + -7x + 9x + 2x2 + 3x2 = 0 Combine like terms: -7x + 9x = 2x -58 + 2x + 2x2 + 3x2 = 0 Combine like terms: 2x2 + 3x2 = 5x2 -58 + 2x + 5x2 = 0 Solving -58 + 2x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -11.6 + 0.4x + x2 = 0 Move the constant term to the right: Add '11.6' to each side of the equation. -11.6 + 0.4x + 11.6 + x2 = 0 + 11.6 Reorder the terms: -11.6 + 11.6 + 0.4x + x2 = 0 + 11.6 Combine like terms: -11.6 + 11.6 = 0.0 0.0 + 0.4x + x2 = 0 + 11.6 0.4x + x2 = 0 + 11.6 Combine like terms: 0 + 11.6 = 11.6 0.4x + x2 = 11.6 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 11.6 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 11.6 + 0.04 Combine like terms: 11.6 + 0.04 = 11.64 0.04 + 0.4x + x2 = 11.64 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 11.64 Calculate the square root of the right side: 3.411744422 Break this problem into two subproblems by setting (x + 0.2) equal to 3.411744422 and -3.411744422.Subproblem 1
x + 0.2 = 3.411744422 Simplifying x + 0.2 = 3.411744422 Reorder the terms: 0.2 + x = 3.411744422 Solving 0.2 + x = 3.411744422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 3.411744422 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 3.411744422 + -0.2 x = 3.411744422 + -0.2 Combine like terms: 3.411744422 + -0.2 = 3.211744422 x = 3.211744422 Simplifying x = 3.211744422Subproblem 2
x + 0.2 = -3.411744422 Simplifying x + 0.2 = -3.411744422 Reorder the terms: 0.2 + x = -3.411744422 Solving 0.2 + x = -3.411744422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -3.411744422 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -3.411744422 + -0.2 x = -3.411744422 + -0.2 Combine like terms: -3.411744422 + -0.2 = -3.611744422 x = -3.611744422 Simplifying x = -3.611744422Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.211744422, -3.611744422}
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