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Simplifying (6x2 + -5x + -45) + (2x2 + 9x) = 0 Reorder the terms: (-45 + -5x + 6x2) + (2x2 + 9x) = 0 Remove parenthesis around (-45 + -5x + 6x2) -45 + -5x + 6x2 + (2x2 + 9x) = 0 Reorder the terms: -45 + -5x + 6x2 + (9x + 2x2) = 0 Remove parenthesis around (9x + 2x2) -45 + -5x + 6x2 + 9x + 2x2 = 0 Reorder the terms: -45 + -5x + 9x + 6x2 + 2x2 = 0 Combine like terms: -5x + 9x = 4x -45 + 4x + 6x2 + 2x2 = 0 Combine like terms: 6x2 + 2x2 = 8x2 -45 + 4x + 8x2 = 0 Solving -45 + 4x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -5.625 + 0.5x + x2 = 0 Move the constant term to the right: Add '5.625' to each side of the equation. -5.625 + 0.5x + 5.625 + x2 = 0 + 5.625 Reorder the terms: -5.625 + 5.625 + 0.5x + x2 = 0 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + 0.5x + x2 = 0 + 5.625 0.5x + x2 = 0 + 5.625 Combine like terms: 0 + 5.625 = 5.625 0.5x + x2 = 5.625 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 5.625 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 5.625 + 0.0625 Combine like terms: 5.625 + 0.0625 = 5.6875 0.0625 + 0.5x + x2 = 5.6875 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 5.6875 Calculate the square root of the right side: 2.384848004 Break this problem into two subproblems by setting (x + 0.25) equal to 2.384848004 and -2.384848004.Subproblem 1
x + 0.25 = 2.384848004 Simplifying x + 0.25 = 2.384848004 Reorder the terms: 0.25 + x = 2.384848004 Solving 0.25 + x = 2.384848004 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 2.384848004 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 2.384848004 + -0.25 x = 2.384848004 + -0.25 Combine like terms: 2.384848004 + -0.25 = 2.134848004 x = 2.134848004 Simplifying x = 2.134848004Subproblem 2
x + 0.25 = -2.384848004 Simplifying x + 0.25 = -2.384848004 Reorder the terms: 0.25 + x = -2.384848004 Solving 0.25 + x = -2.384848004 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -2.384848004 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -2.384848004 + -0.25 x = -2.384848004 + -0.25 Combine like terms: -2.384848004 + -0.25 = -2.634848004 x = -2.634848004 Simplifying x = -2.634848004Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.134848004, -2.634848004}
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