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Simplifying -7x2 + 12x + 28 = 0 Reorder the terms: 28 + 12x + -7x2 = 0 Solving 28 + 12x + -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'. -4 + -1.714285714x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -1.714285714x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -1.714285714x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1.714285714x + x2 = 0 + 4 -1.714285714x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -1.714285714x + x2 = 4 The x term is -1.714285714x. Take half its coefficient (-0.857142857). Square it (0.7346938773) and add it to both sides. Add '0.7346938773' to each side of the equation. -1.714285714x + 0.7346938773 + x2 = 4 + 0.7346938773 Reorder the terms: 0.7346938773 + -1.714285714x + x2 = 4 + 0.7346938773 Combine like terms: 4 + 0.7346938773 = 4.7346938773 0.7346938773 + -1.714285714x + x2 = 4.7346938773 Factor a perfect square on the left side: (x + -0.857142857)(x + -0.857142857) = 4.7346938773 Calculate the square root of the right side: 2.175935173 Break this problem into two subproblems by setting (x + -0.857142857) equal to 2.175935173 and -2.175935173.Subproblem 1
x + -0.857142857 = 2.175935173 Simplifying x + -0.857142857 = 2.175935173 Reorder the terms: -0.857142857 + x = 2.175935173 Solving -0.857142857 + x = 2.175935173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + x = 2.175935173 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + x = 2.175935173 + 0.857142857 x = 2.175935173 + 0.857142857 Combine like terms: 2.175935173 + 0.857142857 = 3.03307803 x = 3.03307803 Simplifying x = 3.03307803Subproblem 2
x + -0.857142857 = -2.175935173 Simplifying x + -0.857142857 = -2.175935173 Reorder the terms: -0.857142857 + x = -2.175935173 Solving -0.857142857 + x = -2.175935173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + x = -2.175935173 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + x = -2.175935173 + 0.857142857 x = -2.175935173 + 0.857142857 Combine like terms: -2.175935173 + 0.857142857 = -1.318792316 x = -1.318792316 Simplifying x = -1.318792316Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.03307803, -1.318792316}
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