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Simplifying 7x2 + 12x + -21 = 0 Reorder the terms: -21 + 12x + 7x2 = 0 Solving -21 + 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'. -3 + 1.714285714x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 1.714285714x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 1.714285714x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 1.714285714x + x2 = 0 + 3 1.714285714x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 1.714285714x + x2 = 3 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 = 3 + 0.7346938773 Reorder the terms: 0.7346938773 + 1.714285714x + x2 = 3 + 0.7346938773 Combine like terms: 3 + 0.7346938773 = 3.7346938773 0.7346938773 + 1.714285714x + x2 = 3.7346938773 Factor a perfect square on the left side: (x + 0.857142857)(x + 0.857142857) = 3.7346938773 Calculate the square root of the right side: 1.932535608 Break this problem into two subproblems by setting (x + 0.857142857) equal to 1.932535608 and -1.932535608.Subproblem 1
x + 0.857142857 = 1.932535608 Simplifying x + 0.857142857 = 1.932535608 Reorder the terms: 0.857142857 + x = 1.932535608 Solving 0.857142857 + x = 1.932535608 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 = 1.932535608 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + x = 1.932535608 + -0.857142857 x = 1.932535608 + -0.857142857 Combine like terms: 1.932535608 + -0.857142857 = 1.075392751 x = 1.075392751 Simplifying x = 1.075392751Subproblem 2
x + 0.857142857 = -1.932535608 Simplifying x + 0.857142857 = -1.932535608 Reorder the terms: 0.857142857 + x = -1.932535608 Solving 0.857142857 + x = -1.932535608 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 = -1.932535608 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + x = -1.932535608 + -0.857142857 x = -1.932535608 + -0.857142857 Combine like terms: -1.932535608 + -0.857142857 = -2.789678465 x = -2.789678465 Simplifying x = -2.789678465Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.075392751, -2.789678465}
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