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Simplifying 2x + 5x(x + 1) = 147 Reorder the terms: 2x + 5x(1 + x) = 147 2x + (1 * 5x + x * 5x) = 147 2x + (5x + 5x2) = 147 Combine like terms: 2x + 5x = 7x 7x + 5x2 = 147 Solving 7x + 5x2 = 147 Solving for variable 'x'. Reorder the terms: -147 + 7x + 5x2 = 147 + -147 Combine like terms: 147 + -147 = 0 -147 + 7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -29.4 + 1.4x + x2 = 0 Move the constant term to the right: Add '29.4' to each side of the equation. -29.4 + 1.4x + 29.4 + x2 = 0 + 29.4 Reorder the terms: -29.4 + 29.4 + 1.4x + x2 = 0 + 29.4 Combine like terms: -29.4 + 29.4 = 0.0 0.0 + 1.4x + x2 = 0 + 29.4 1.4x + x2 = 0 + 29.4 Combine like terms: 0 + 29.4 = 29.4 1.4x + x2 = 29.4 The x term is 1.4x. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4x + 0.49 + x2 = 29.4 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = 29.4 + 0.49 Combine like terms: 29.4 + 0.49 = 29.89 0.49 + 1.4x + x2 = 29.89 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = 29.89 Calculate the square root of the right side: 5.467174773 Break this problem into two subproblems by setting (x + 0.7) equal to 5.467174773 and -5.467174773.Subproblem 1
x + 0.7 = 5.467174773 Simplifying x + 0.7 = 5.467174773 Reorder the terms: 0.7 + x = 5.467174773 Solving 0.7 + x = 5.467174773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = 5.467174773 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 5.467174773 + -0.7 x = 5.467174773 + -0.7 Combine like terms: 5.467174773 + -0.7 = 4.767174773 x = 4.767174773 Simplifying x = 4.767174773Subproblem 2
x + 0.7 = -5.467174773 Simplifying x + 0.7 = -5.467174773 Reorder the terms: 0.7 + x = -5.467174773 Solving 0.7 + x = -5.467174773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = -5.467174773 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -5.467174773 + -0.7 x = -5.467174773 + -0.7 Combine like terms: -5.467174773 + -0.7 = -6.167174773 x = -6.167174773 Simplifying x = -6.167174773Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.767174773, -6.167174773}
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