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Simplifying (4x2 + -4x + 21) + (3x2 + 8x + -69) = 0 Reorder the terms: (21 + -4x + 4x2) + (3x2 + 8x + -69) = 0 Remove parenthesis around (21 + -4x + 4x2) 21 + -4x + 4x2 + (3x2 + 8x + -69) = 0 Reorder the terms: 21 + -4x + 4x2 + (-69 + 8x + 3x2) = 0 Remove parenthesis around (-69 + 8x + 3x2) 21 + -4x + 4x2 + -69 + 8x + 3x2 = 0 Reorder the terms: 21 + -69 + -4x + 8x + 4x2 + 3x2 = 0 Combine like terms: 21 + -69 = -48 -48 + -4x + 8x + 4x2 + 3x2 = 0 Combine like terms: -4x + 8x = 4x -48 + 4x + 4x2 + 3x2 = 0 Combine like terms: 4x2 + 3x2 = 7x2 -48 + 4x + 7x2 = 0 Solving -48 + 4x + 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'. -6.857142857 + 0.5714285714x + x2 = 0 Move the constant term to the right: Add '6.857142857' to each side of the equation. -6.857142857 + 0.5714285714x + 6.857142857 + x2 = 0 + 6.857142857 Reorder the terms: -6.857142857 + 6.857142857 + 0.5714285714x + x2 = 0 + 6.857142857 Combine like terms: -6.857142857 + 6.857142857 = 0.000000000 0.000000000 + 0.5714285714x + x2 = 0 + 6.857142857 0.5714285714x + x2 = 0 + 6.857142857 Combine like terms: 0 + 6.857142857 = 6.857142857 0.5714285714x + x2 = 6.857142857 The x term is 0.5714285714x. Take half its coefficient (0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. 0.5714285714x + 0.08163265305 + x2 = 6.857142857 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714x + x2 = 6.857142857 + 0.08163265305 Combine like terms: 6.857142857 + 0.08163265305 = 6.93877551005 0.08163265305 + 0.5714285714x + x2 = 6.93877551005 Factor a perfect square on the left side: (x + 0.2857142857)(x + 0.2857142857) = 6.93877551005 Calculate the square root of the right side: 2.634155559 Break this problem into two subproblems by setting (x + 0.2857142857) equal to 2.634155559 and -2.634155559.Subproblem 1
x + 0.2857142857 = 2.634155559 Simplifying x + 0.2857142857 = 2.634155559 Reorder the terms: 0.2857142857 + x = 2.634155559 Solving 0.2857142857 + x = 2.634155559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = 2.634155559 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = 2.634155559 + -0.2857142857 x = 2.634155559 + -0.2857142857 Combine like terms: 2.634155559 + -0.2857142857 = 2.3484412733 x = 2.3484412733 Simplifying x = 2.3484412733Subproblem 2
x + 0.2857142857 = -2.634155559 Simplifying x + 0.2857142857 = -2.634155559 Reorder the terms: 0.2857142857 + x = -2.634155559 Solving 0.2857142857 + x = -2.634155559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = -2.634155559 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = -2.634155559 + -0.2857142857 x = -2.634155559 + -0.2857142857 Combine like terms: -2.634155559 + -0.2857142857 = -2.9198698447 x = -2.9198698447 Simplifying x = -2.9198698447Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3484412733, -2.9198698447}
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