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Simplifying (4x2 + -2x + -29) + (3x2 + 9x) = 0 Reorder the terms: (-29 + -2x + 4x2) + (3x2 + 9x) = 0 Remove parenthesis around (-29 + -2x + 4x2) -29 + -2x + 4x2 + (3x2 + 9x) = 0 Reorder the terms: -29 + -2x + 4x2 + (9x + 3x2) = 0 Remove parenthesis around (9x + 3x2) -29 + -2x + 4x2 + 9x + 3x2 = 0 Reorder the terms: -29 + -2x + 9x + 4x2 + 3x2 = 0 Combine like terms: -2x + 9x = 7x -29 + 7x + 4x2 + 3x2 = 0 Combine like terms: 4x2 + 3x2 = 7x2 -29 + 7x + 7x2 = 0 Solving -29 + 7x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -4.142857143 + x + x2 = 0 Move the constant term to the right: Add '4.142857143' to each side of the equation. -4.142857143 + x + 4.142857143 + x2 = 0 + 4.142857143 Reorder the terms: -4.142857143 + 4.142857143 + x + x2 = 0 + 4.142857143 Combine like terms: -4.142857143 + 4.142857143 = 0.000000000 0.000000000 + x + x2 = 0 + 4.142857143 x + x2 = 0 + 4.142857143 Combine like terms: 0 + 4.142857143 = 4.142857143 x + x2 = 4.142857143 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 4.142857143 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 4.142857143 + 0.25 Combine like terms: 4.142857143 + 0.25 = 4.392857143 1.25 + x2 = 4.392857143 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 4.392857143 Calculate the square root of the right side: 2.095914393 Break this problem into two subproblems by setting (x + 0.5) equal to 2.095914393 and -2.095914393.Subproblem 1
x + 0.5 = 2.095914393 Simplifying x + 0.5 = 2.095914393 Reorder the terms: 0.5 + x = 2.095914393 Solving 0.5 + x = 2.095914393 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.095914393 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.095914393 + -0.5 x = 2.095914393 + -0.5 Combine like terms: 2.095914393 + -0.5 = 1.595914393 x = 1.595914393 Simplifying x = 1.595914393Subproblem 2
x + 0.5 = -2.095914393 Simplifying x + 0.5 = -2.095914393 Reorder the terms: 0.5 + x = -2.095914393 Solving 0.5 + x = -2.095914393 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.095914393 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.095914393 + -0.5 x = -2.095914393 + -0.5 Combine like terms: -2.095914393 + -0.5 = -2.595914393 x = -2.595914393 Simplifying x = -2.595914393Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.595914393, -2.595914393}
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