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Simplifying 4.9x(6 + -1x) + 36 = 2(x + 9) + -1x2 (6 * 4.9x + -1x * 4.9x) + 36 = 2(x + 9) + -1x2 (29.4x + -4.9x2) + 36 = 2(x + 9) + -1x2 Reorder the terms: 36 + 29.4x + -4.9x2 = 2(x + 9) + -1x2 Reorder the terms: 36 + 29.4x + -4.9x2 = 2(9 + x) + -1x2 36 + 29.4x + -4.9x2 = (9 * 2 + x * 2) + -1x2 36 + 29.4x + -4.9x2 = (18 + 2x) + -1x2 Solving 36 + 29.4x + -4.9x2 = 18 + 2x + -1x2 Solving for variable 'x'. Reorder the terms: 36 + -18 + 29.4x + -2x + -4.9x2 + x2 = 18 + 2x + -1x2 + -18 + -2x + x2 Combine like terms: 36 + -18 = 18 18 + 29.4x + -2x + -4.9x2 + x2 = 18 + 2x + -1x2 + -18 + -2x + x2 Combine like terms: 29.4x + -2x = 27.4x 18 + 27.4x + -4.9x2 + x2 = 18 + 2x + -1x2 + -18 + -2x + x2 Combine like terms: -4.9x2 + x2 = -3.9x2 18 + 27.4x + -3.9x2 = 18 + 2x + -1x2 + -18 + -2x + x2 Reorder the terms: 18 + 27.4x + -3.9x2 = 18 + -18 + 2x + -2x + -1x2 + x2 Combine like terms: 18 + -18 = 0 18 + 27.4x + -3.9x2 = 0 + 2x + -2x + -1x2 + x2 18 + 27.4x + -3.9x2 = 2x + -2x + -1x2 + x2 Combine like terms: 2x + -2x = 0 18 + 27.4x + -3.9x2 = 0 + -1x2 + x2 18 + 27.4x + -3.9x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 18 + 27.4x + -3.9x2 = 0 Begin completing the square. Divide all terms by -3.9 the coefficient of the squared term: Divide each side by '-3.9'. -4.615384615 + -7.025641026x + x2 = 0 Move the constant term to the right: Add '4.615384615' to each side of the equation. -4.615384615 + -7.025641026x + 4.615384615 + x2 = 0 + 4.615384615 Reorder the terms: -4.615384615 + 4.615384615 + -7.025641026x + x2 = 0 + 4.615384615 Combine like terms: -4.615384615 + 4.615384615 = 0.000000000 0.000000000 + -7.025641026x + x2 = 0 + 4.615384615 -7.025641026x + x2 = 0 + 4.615384615 Combine like terms: 0 + 4.615384615 = 4.615384615 -7.025641026x + x2 = 4.615384615 The x term is -7.025641026x. Take half its coefficient (-3.512820513). Square it (12.33990796) and add it to both sides. Add '12.33990796' to each side of the equation. -7.025641026x + 12.33990796 + x2 = 4.615384615 + 12.33990796 Reorder the terms: 12.33990796 + -7.025641026x + x2 = 4.615384615 + 12.33990796 Combine like terms: 4.615384615 + 12.33990796 = 16.955292575 12.33990796 + -7.025641026x + x2 = 16.955292575 Factor a perfect square on the left side: (x + -3.512820513)(x + -3.512820513) = 16.955292575 Calculate the square root of the right side: 4.117680485 Break this problem into two subproblems by setting (x + -3.512820513) equal to 4.117680485 and -4.117680485.Subproblem 1
x + -3.512820513 = 4.117680485 Simplifying x + -3.512820513 = 4.117680485 Reorder the terms: -3.512820513 + x = 4.117680485 Solving -3.512820513 + x = 4.117680485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.512820513' to each side of the equation. -3.512820513 + 3.512820513 + x = 4.117680485 + 3.512820513 Combine like terms: -3.512820513 + 3.512820513 = 0.000000000 0.000000000 + x = 4.117680485 + 3.512820513 x = 4.117680485 + 3.512820513 Combine like terms: 4.117680485 + 3.512820513 = 7.630500998 x = 7.630500998 Simplifying x = 7.630500998Subproblem 2
x + -3.512820513 = -4.117680485 Simplifying x + -3.512820513 = -4.117680485 Reorder the terms: -3.512820513 + x = -4.117680485 Solving -3.512820513 + x = -4.117680485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.512820513' to each side of the equation. -3.512820513 + 3.512820513 + x = -4.117680485 + 3.512820513 Combine like terms: -3.512820513 + 3.512820513 = 0.000000000 0.000000000 + x = -4.117680485 + 3.512820513 x = -4.117680485 + 3.512820513 Combine like terms: -4.117680485 + 3.512820513 = -0.604859972 x = -0.604859972 Simplifying x = -0.604859972Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.630500998, -0.604859972}
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