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Simplifying 7x2 + -4x + -48 = 0 Reorder the terms: -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 = 2.9198698447 x = 2.9198698447 Simplifying x = 2.9198698447Subproblem 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 = -2.3484412733 x = -2.3484412733 Simplifying x = -2.3484412733Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.9198698447, -2.3484412733}
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