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Simplifying 4x + 3(x + 7) = 1.4x(x + 7) Reorder the terms: 4x + 3(7 + x) = 1.4x(x + 7) 4x + (7 * 3 + x * 3) = 1.4x(x + 7) 4x + (21 + 3x) = 1.4x(x + 7) Reorder the terms: 21 + 4x + 3x = 1.4x(x + 7) Combine like terms: 4x + 3x = 7x 21 + 7x = 1.4x(x + 7) Reorder the terms: 21 + 7x = 1.4x(7 + x) 21 + 7x = (7 * 1.4x + x * 1.4x) 21 + 7x = (9.8x + 1.4x2) Solving 21 + 7x = 9.8x + 1.4x2 Solving for variable 'x'. Combine like terms: 7x + -9.8x = -2.8x 21 + -2.8x + -1.4x2 = 9.8x + 1.4x2 + -9.8x + -1.4x2 Reorder the terms: 21 + -2.8x + -1.4x2 = 9.8x + -9.8x + 1.4x2 + -1.4x2 Combine like terms: 9.8x + -9.8x = 0.0 21 + -2.8x + -1.4x2 = 0.0 + 1.4x2 + -1.4x2 21 + -2.8x + -1.4x2 = 1.4x2 + -1.4x2 Combine like terms: 1.4x2 + -1.4x2 = 0.0 21 + -2.8x + -1.4x2 = 0.0 Begin completing the square. Divide all terms by -1.4 the coefficient of the squared term: Divide each side by '-1.4'. -15 + 2x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 2x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 2x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 2x + x2 = 0 + 15 2x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 2x + x2 = 15 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 15 + 1 Reorder the terms: 1 + 2x + x2 = 15 + 1 Combine like terms: 15 + 1 = 16 1 + 2x + x2 = 16 Factor a perfect square on the left side: (x + 1)(x + 1) = 16 Calculate the square root of the right side: 4 Break this problem into two subproblems by setting (x + 1) equal to 4 and -4.Subproblem 1
x + 1 = 4 Simplifying x + 1 = 4 Reorder the terms: 1 + x = 4 Solving 1 + x = 4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 4 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4 + -1 x = 4 + -1 Combine like terms: 4 + -1 = 3 x = 3 Simplifying x = 3Subproblem 2
x + 1 = -4 Simplifying x + 1 = -4 Reorder the terms: 1 + x = -4 Solving 1 + x = -4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -4 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4 + -1 x = -4 + -1 Combine like terms: -4 + -1 = -5 x = -5 Simplifying x = -5Solution
The solution to the problem is based on the solutions from the subproblems. x = {3, -5}
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