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Simplifying x(x + 4x) = 7(x + 3) + 7 Combine like terms: x + 4x = 5x x(5x) = 7(x + 3) + 7 Remove parenthesis around (5x) x * 5x = 7(x + 3) + 7 Reorder the terms for easier multiplication: 5x * x = 7(x + 3) + 7 Multiply x * x 5x2 = 7(x + 3) + 7 Reorder the terms: 5x2 = 7(3 + x) + 7 5x2 = (3 * 7 + x * 7) + 7 5x2 = (21 + 7x) + 7 Reorder the terms: 5x2 = 21 + 7 + 7x Combine like terms: 21 + 7 = 28 5x2 = 28 + 7x Solving 5x2 = 28 + 7x Solving for variable 'x'. Reorder the terms: -28 + -7x + 5x2 = 28 + 7x + -28 + -7x Reorder the terms: -28 + -7x + 5x2 = 28 + -28 + 7x + -7x Combine like terms: 28 + -28 = 0 -28 + -7x + 5x2 = 0 + 7x + -7x -28 + -7x + 5x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -28 + -7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5.6 + -1.4x + x2 = 0 Move the constant term to the right: Add '5.6' to each side of the equation. -5.6 + -1.4x + 5.6 + x2 = 0 + 5.6 Reorder the terms: -5.6 + 5.6 + -1.4x + x2 = 0 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + -1.4x + x2 = 0 + 5.6 -1.4x + x2 = 0 + 5.6 Combine like terms: 0 + 5.6 = 5.6 -1.4x + x2 = 5.6 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 = 5.6 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = 5.6 + 0.49 Combine like terms: 5.6 + 0.49 = 6.09 0.49 + -1.4x + x2 = 6.09 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 6.09 Calculate the square root of the right side: 2.467792536 Break this problem into two subproblems by setting (x + -0.7) equal to 2.467792536 and -2.467792536.Subproblem 1
x + -0.7 = 2.467792536 Simplifying x + -0.7 = 2.467792536 Reorder the terms: -0.7 + x = 2.467792536 Solving -0.7 + x = 2.467792536 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 = 2.467792536 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 2.467792536 + 0.7 x = 2.467792536 + 0.7 Combine like terms: 2.467792536 + 0.7 = 3.167792536 x = 3.167792536 Simplifying x = 3.167792536Subproblem 2
x + -0.7 = -2.467792536 Simplifying x + -0.7 = -2.467792536 Reorder the terms: -0.7 + x = -2.467792536 Solving -0.7 + x = -2.467792536 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 = -2.467792536 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -2.467792536 + 0.7 x = -2.467792536 + 0.7 Combine like terms: -2.467792536 + 0.7 = -1.767792536 x = -1.767792536 Simplifying x = -1.767792536Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.167792536, -1.767792536}
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