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Simplifying 7x + 3(x2 + -5) = x + -3 Reorder the terms: 7x + 3(-5 + x2) = x + -3 7x + (-5 * 3 + x2 * 3) = x + -3 7x + (-15 + 3x2) = x + -3 Reorder the terms: -15 + 7x + 3x2 = x + -3 Reorder the terms: -15 + 7x + 3x2 = -3 + x Solving -15 + 7x + 3x2 = -3 + x Solving for variable 'x'. Reorder the terms: -15 + 3 + 7x + -1x + 3x2 = -3 + x + 3 + -1x Combine like terms: -15 + 3 = -12 -12 + 7x + -1x + 3x2 = -3 + x + 3 + -1x Combine like terms: 7x + -1x = 6x -12 + 6x + 3x2 = -3 + x + 3 + -1x Reorder the terms: -12 + 6x + 3x2 = -3 + 3 + x + -1x Combine like terms: -3 + 3 = 0 -12 + 6x + 3x2 = 0 + x + -1x -12 + 6x + 3x2 = x + -1x Combine like terms: x + -1x = 0 -12 + 6x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 2x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + 2x + x2)' equal to zero and attempt to solve: Simplifying -4 + 2x + x2 = 0 Solving -4 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 2x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 2x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 2x + x2 = 0 + 4 2x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 2x + x2 = 4 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 = 4 + 1 Reorder the terms: 1 + 2x + x2 = 4 + 1 Combine like terms: 4 + 1 = 5 1 + 2x + x2 = 5 Factor a perfect square on the left side: (x + 1)(x + 1) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x + 1) equal to 2.236067978 and -2.236067978.Subproblem 1
x + 1 = 2.236067978 Simplifying x + 1 = 2.236067978 Reorder the terms: 1 + x = 2.236067978 Solving 1 + x = 2.236067978 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 = 2.236067978 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.236067978 + -1 x = 2.236067978 + -1 Combine like terms: 2.236067978 + -1 = 1.236067978 x = 1.236067978 Simplifying x = 1.236067978Subproblem 2
x + 1 = -2.236067978 Simplifying x + 1 = -2.236067978 Reorder the terms: 1 + x = -2.236067978 Solving 1 + x = -2.236067978 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 = -2.236067978 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.236067978 + -1 x = -2.236067978 + -1 Combine like terms: -2.236067978 + -1 = -3.236067978 x = -3.236067978 Simplifying x = -3.236067978Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.236067978, -3.236067978}Solution
x = {1.236067978, -3.236067978}
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