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Simplifying 14x(3x + -7) = 29 Reorder the terms: 14x(-7 + 3x) = 29 (-7 * 14x + 3x * 14x) = 29 (-98x + 42x2) = 29 Solving -98x + 42x2 = 29 Solving for variable 'x'. Reorder the terms: -29 + -98x + 42x2 = 29 + -29 Combine like terms: 29 + -29 = 0 -29 + -98x + 42x2 = 0 Begin completing the square. Divide all terms by 42 the coefficient of the squared term: Divide each side by '42'. -0.6904761905 + -2.333333333x + x2 = 0 Move the constant term to the right: Add '0.6904761905' to each side of the equation. -0.6904761905 + -2.333333333x + 0.6904761905 + x2 = 0 + 0.6904761905 Reorder the terms: -0.6904761905 + 0.6904761905 + -2.333333333x + x2 = 0 + 0.6904761905 Combine like terms: -0.6904761905 + 0.6904761905 = 0.0000000000 0.0000000000 + -2.333333333x + x2 = 0 + 0.6904761905 -2.333333333x + x2 = 0 + 0.6904761905 Combine like terms: 0 + 0.6904761905 = 0.6904761905 -2.333333333x + x2 = 0.6904761905 The x term is -2.333333333x. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333x + 1.361111112 + x2 = 0.6904761905 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333x + x2 = 0.6904761905 + 1.361111112 Combine like terms: 0.6904761905 + 1.361111112 = 2.0515873025 1.361111112 + -2.333333333x + x2 = 2.0515873025 Factor a perfect square on the left side: (x + -1.166666667)(x + -1.166666667) = 2.0515873025 Calculate the square root of the right side: 1.432336309 Break this problem into two subproblems by setting (x + -1.166666667) equal to 1.432336309 and -1.432336309.Subproblem 1
x + -1.166666667 = 1.432336309 Simplifying x + -1.166666667 = 1.432336309 Reorder the terms: -1.166666667 + x = 1.432336309 Solving -1.166666667 + x = 1.432336309 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = 1.432336309 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = 1.432336309 + 1.166666667 x = 1.432336309 + 1.166666667 Combine like terms: 1.432336309 + 1.166666667 = 2.599002976 x = 2.599002976 Simplifying x = 2.599002976Subproblem 2
x + -1.166666667 = -1.432336309 Simplifying x + -1.166666667 = -1.432336309 Reorder the terms: -1.166666667 + x = -1.432336309 Solving -1.166666667 + x = -1.432336309 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = -1.432336309 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = -1.432336309 + 1.166666667 x = -1.432336309 + 1.166666667 Combine like terms: -1.432336309 + 1.166666667 = -0.265669642 x = -0.265669642 Simplifying x = -0.265669642Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.599002976, -0.265669642}
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