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Simplifying (4x2 + -6x + 27) + (2x2 + 9x + -42) = 0 Reorder the terms: (27 + -6x + 4x2) + (2x2 + 9x + -42) = 0 Remove parenthesis around (27 + -6x + 4x2) 27 + -6x + 4x2 + (2x2 + 9x + -42) = 0 Reorder the terms: 27 + -6x + 4x2 + (-42 + 9x + 2x2) = 0 Remove parenthesis around (-42 + 9x + 2x2) 27 + -6x + 4x2 + -42 + 9x + 2x2 = 0 Reorder the terms: 27 + -42 + -6x + 9x + 4x2 + 2x2 = 0 Combine like terms: 27 + -42 = -15 -15 + -6x + 9x + 4x2 + 2x2 = 0 Combine like terms: -6x + 9x = 3x -15 + 3x + 4x2 + 2x2 = 0 Combine like terms: 4x2 + 2x2 = 6x2 -15 + 3x + 6x2 = 0 Solving -15 + 3x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + x + 2x2)' equal to zero and attempt to solve: Simplifying -5 + x + 2x2 = 0 Solving -5 + x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + 0.5x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 0.5x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 0.5x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 0.5x + x2 = 0 + 2.5 0.5x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 0.5x + x2 = 2.5 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. 0.5x + 0.25 + x2 = 2.5 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 2.5 + 0.25 Combine like terms: 2.5 + 0.25 = 2.75 0.25 + 0.5x + x2 = 2.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (x + 0.5) equal to 1.658312395 and -1.658312395.Subproblem 1
x + 0.5 = 1.658312395 Simplifying x + 0.5 = 1.658312395 Reorder the terms: 0.5 + x = 1.658312395 Solving 0.5 + x = 1.658312395 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 = 1.658312395 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.658312395 + -0.5 x = 1.658312395 + -0.5 Combine like terms: 1.658312395 + -0.5 = 1.158312395 x = 1.158312395 Simplifying x = 1.158312395Subproblem 2
x + 0.5 = -1.658312395 Simplifying x + 0.5 = -1.658312395 Reorder the terms: 0.5 + x = -1.658312395 Solving 0.5 + x = -1.658312395 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 = -1.658312395 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.658312395 + -0.5 x = -1.658312395 + -0.5 Combine like terms: -1.658312395 + -0.5 = -2.158312395 x = -2.158312395 Simplifying x = -2.158312395Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.158312395, -2.158312395}Solution
x = {1.158312395, -2.158312395}
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