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Simplifying 7x(3 + x) = 136 (3 * 7x + x * 7x) = 136 (21x + 7x2) = 136 Solving 21x + 7x2 = 136 Solving for variable 'x'. Reorder the terms: -136 + 21x + 7x2 = 136 + -136 Combine like terms: 136 + -136 = 0 -136 + 21x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -19.42857143 + 3x + x2 = 0 Move the constant term to the right: Add '19.42857143' to each side of the equation. -19.42857143 + 3x + 19.42857143 + x2 = 0 + 19.42857143 Reorder the terms: -19.42857143 + 19.42857143 + 3x + x2 = 0 + 19.42857143 Combine like terms: -19.42857143 + 19.42857143 = 0.00000000 0.00000000 + 3x + x2 = 0 + 19.42857143 3x + x2 = 0 + 19.42857143 Combine like terms: 0 + 19.42857143 = 19.42857143 3x + x2 = 19.42857143 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 19.42857143 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 19.42857143 + 2.25 Combine like terms: 19.42857143 + 2.25 = 21.67857143 2.25 + 3x + x2 = 21.67857143 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 21.67857143 Calculate the square root of the right side: 4.656025282 Break this problem into two subproblems by setting (x + 1.5) equal to 4.656025282 and -4.656025282.Subproblem 1
x + 1.5 = 4.656025282 Simplifying x + 1.5 = 4.656025282 Reorder the terms: 1.5 + x = 4.656025282 Solving 1.5 + x = 4.656025282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 4.656025282 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 4.656025282 + -1.5 x = 4.656025282 + -1.5 Combine like terms: 4.656025282 + -1.5 = 3.156025282 x = 3.156025282 Simplifying x = 3.156025282Subproblem 2
x + 1.5 = -4.656025282 Simplifying x + 1.5 = -4.656025282 Reorder the terms: 1.5 + x = -4.656025282 Solving 1.5 + x = -4.656025282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -4.656025282 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -4.656025282 + -1.5 x = -4.656025282 + -1.5 Combine like terms: -4.656025282 + -1.5 = -6.156025282 x = -6.156025282 Simplifying x = -6.156025282Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.156025282, -6.156025282}
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