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Simplifying 4x + 12 = 7x2 Reorder the terms: 12 + 4x = 7x2 Solving 12 + 4x = 7x2 Solving for variable 'x'. Combine like terms: 7x2 + -7x2 = 0 12 + 4x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -1.714285714 + -0.5714285714x + x2 = 0 Move the constant term to the right: Add '1.714285714' to each side of the equation. -1.714285714 + -0.5714285714x + 1.714285714 + x2 = 0 + 1.714285714 Reorder the terms: -1.714285714 + 1.714285714 + -0.5714285714x + x2 = 0 + 1.714285714 Combine like terms: -1.714285714 + 1.714285714 = 0.000000000 0.000000000 + -0.5714285714x + x2 = 0 + 1.714285714 -0.5714285714x + x2 = 0 + 1.714285714 Combine like terms: 0 + 1.714285714 = 1.714285714 -0.5714285714x + x2 = 1.714285714 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 = 1.714285714 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714x + x2 = 1.714285714 + 0.08163265305 Combine like terms: 1.714285714 + 0.08163265305 = 1.79591836705 0.08163265305 + -0.5714285714x + x2 = 1.79591836705 Factor a perfect square on the left side: (x + -0.2857142857)(x + -0.2857142857) = 1.79591836705 Calculate the square root of the right side: 1.340118788 Break this problem into two subproblems by setting (x + -0.2857142857) equal to 1.340118788 and -1.340118788.Subproblem 1
x + -0.2857142857 = 1.340118788 Simplifying x + -0.2857142857 = 1.340118788 Reorder the terms: -0.2857142857 + x = 1.340118788 Solving -0.2857142857 + x = 1.340118788 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 = 1.340118788 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = 1.340118788 + 0.2857142857 x = 1.340118788 + 0.2857142857 Combine like terms: 1.340118788 + 0.2857142857 = 1.6258330737 x = 1.6258330737 Simplifying x = 1.6258330737Subproblem 2
x + -0.2857142857 = -1.340118788 Simplifying x + -0.2857142857 = -1.340118788 Reorder the terms: -0.2857142857 + x = -1.340118788 Solving -0.2857142857 + x = -1.340118788 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 = -1.340118788 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = -1.340118788 + 0.2857142857 x = -1.340118788 + 0.2857142857 Combine like terms: -1.340118788 + 0.2857142857 = -1.0544045023 x = -1.0544045023 Simplifying x = -1.0544045023Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6258330737, -1.0544045023}
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