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Simplifying 12x + 7x2 + 21 = 34 Reorder the terms: 21 + 12x + 7x2 = 34 Solving 21 + 12x + 7x2 = 34 Solving for variable 'x'. Reorder the terms: 21 + -34 + 12x + 7x2 = 34 + -34 Combine like terms: 21 + -34 = -13 -13 + 12x + 7x2 = 34 + -34 Combine like terms: 34 + -34 = 0 -13 + 12x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.857142857 + 1.714285714x + x2 = 0 Move the constant term to the right: Add '1.857142857' to each side of the equation. -1.857142857 + 1.714285714x + 1.857142857 + x2 = 0 + 1.857142857 Reorder the terms: -1.857142857 + 1.857142857 + 1.714285714x + x2 = 0 + 1.857142857 Combine like terms: -1.857142857 + 1.857142857 = 0.000000000 0.000000000 + 1.714285714x + x2 = 0 + 1.857142857 1.714285714x + x2 = 0 + 1.857142857 Combine like terms: 0 + 1.857142857 = 1.857142857 1.714285714x + x2 = 1.857142857 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 = 1.857142857 + 0.7346938773 Reorder the terms: 0.7346938773 + 1.714285714x + x2 = 1.857142857 + 0.7346938773 Combine like terms: 1.857142857 + 0.7346938773 = 2.5918367343 0.7346938773 + 1.714285714x + x2 = 2.5918367343 Factor a perfect square on the left side: (x + 0.857142857)(x + 0.857142857) = 2.5918367343 Calculate the square root of the right side: 1.609918238 Break this problem into two subproblems by setting (x + 0.857142857) equal to 1.609918238 and -1.609918238.Subproblem 1
x + 0.857142857 = 1.609918238 Simplifying x + 0.857142857 = 1.609918238 Reorder the terms: 0.857142857 + x = 1.609918238 Solving 0.857142857 + x = 1.609918238 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 = 1.609918238 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + x = 1.609918238 + -0.857142857 x = 1.609918238 + -0.857142857 Combine like terms: 1.609918238 + -0.857142857 = 0.752775381 x = 0.752775381 Simplifying x = 0.752775381Subproblem 2
x + 0.857142857 = -1.609918238 Simplifying x + 0.857142857 = -1.609918238 Reorder the terms: 0.857142857 + x = -1.609918238 Solving 0.857142857 + x = -1.609918238 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 = -1.609918238 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + x = -1.609918238 + -0.857142857 x = -1.609918238 + -0.857142857 Combine like terms: -1.609918238 + -0.857142857 = -2.467061095 x = -2.467061095 Simplifying x = -2.467061095Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.752775381, -2.467061095}
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