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Simplifying 5x * 3(x + -1) = 7x + -2 Reorder the terms: 5x * 3(-1 + x) = 7x + -2 Reorder the terms for easier multiplication: 5 * 3x(-1 + x) = 7x + -2 Multiply 5 * 3 15x(-1 + x) = 7x + -2 (-1 * 15x + x * 15x) = 7x + -2 (-15x + 15x2) = 7x + -2 Reorder the terms: -15x + 15x2 = -2 + 7x Solving -15x + 15x2 = -2 + 7x Solving for variable 'x'. Reorder the terms: 2 + -15x + -7x + 15x2 = -2 + 7x + 2 + -7x Combine like terms: -15x + -7x = -22x 2 + -22x + 15x2 = -2 + 7x + 2 + -7x Reorder the terms: 2 + -22x + 15x2 = -2 + 2 + 7x + -7x Combine like terms: -2 + 2 = 0 2 + -22x + 15x2 = 0 + 7x + -7x 2 + -22x + 15x2 = 7x + -7x Combine like terms: 7x + -7x = 0 2 + -22x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 0.1333333333 + -1.466666667x + x2 = 0 Move the constant term to the right: Add '-0.1333333333' to each side of the equation. 0.1333333333 + -1.466666667x + -0.1333333333 + x2 = 0 + -0.1333333333 Reorder the terms: 0.1333333333 + -0.1333333333 + -1.466666667x + x2 = 0 + -0.1333333333 Combine like terms: 0.1333333333 + -0.1333333333 = 0.0000000000 0.0000000000 + -1.466666667x + x2 = 0 + -0.1333333333 -1.466666667x + x2 = 0 + -0.1333333333 Combine like terms: 0 + -0.1333333333 = -0.1333333333 -1.466666667x + x2 = -0.1333333333 The x term is -1.466666667x. Take half its coefficient (-0.7333333335). Square it (0.5377777780) and add it to both sides. Add '0.5377777780' to each side of the equation. -1.466666667x + 0.5377777780 + x2 = -0.1333333333 + 0.5377777780 Reorder the terms: 0.5377777780 + -1.466666667x + x2 = -0.1333333333 + 0.5377777780 Combine like terms: -0.1333333333 + 0.5377777780 = 0.4044444447 0.5377777780 + -1.466666667x + x2 = 0.4044444447 Factor a perfect square on the left side: (x + -0.7333333335)(x + -0.7333333335) = 0.4044444447 Calculate the square root of the right side: 0.635959468 Break this problem into two subproblems by setting (x + -0.7333333335) equal to 0.635959468 and -0.635959468.Subproblem 1
x + -0.7333333335 = 0.635959468 Simplifying x + -0.7333333335 = 0.635959468 Reorder the terms: -0.7333333335 + x = 0.635959468 Solving -0.7333333335 + x = 0.635959468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7333333335' to each side of the equation. -0.7333333335 + 0.7333333335 + x = 0.635959468 + 0.7333333335 Combine like terms: -0.7333333335 + 0.7333333335 = 0.0000000000 0.0000000000 + x = 0.635959468 + 0.7333333335 x = 0.635959468 + 0.7333333335 Combine like terms: 0.635959468 + 0.7333333335 = 1.3692928015 x = 1.3692928015 Simplifying x = 1.3692928015Subproblem 2
x + -0.7333333335 = -0.635959468 Simplifying x + -0.7333333335 = -0.635959468 Reorder the terms: -0.7333333335 + x = -0.635959468 Solving -0.7333333335 + x = -0.635959468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7333333335' to each side of the equation. -0.7333333335 + 0.7333333335 + x = -0.635959468 + 0.7333333335 Combine like terms: -0.7333333335 + 0.7333333335 = 0.0000000000 0.0000000000 + x = -0.635959468 + 0.7333333335 x = -0.635959468 + 0.7333333335 Combine like terms: -0.635959468 + 0.7333333335 = 0.0973738655 x = 0.0973738655 Simplifying x = 0.0973738655Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3692928015, 0.0973738655}
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