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Simplifying 3x + 7 = 2x(5x + -4) Reorder the terms: 7 + 3x = 2x(5x + -4) Reorder the terms: 7 + 3x = 2x(-4 + 5x) 7 + 3x = (-4 * 2x + 5x * 2x) 7 + 3x = (-8x + 10x2) Solving 7 + 3x = -8x + 10x2 Solving for variable 'x'. Combine like terms: 3x + 8x = 11x 7 + 11x + -10x2 = -8x + 10x2 + 8x + -10x2 Reorder the terms: 7 + 11x + -10x2 = -8x + 8x + 10x2 + -10x2 Combine like terms: -8x + 8x = 0 7 + 11x + -10x2 = 0 + 10x2 + -10x2 7 + 11x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 7 + 11x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -0.7 + -1.1x + x2 = 0 Move the constant term to the right: Add '0.7' to each side of the equation. -0.7 + -1.1x + 0.7 + x2 = 0 + 0.7 Reorder the terms: -0.7 + 0.7 + -1.1x + x2 = 0 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + -1.1x + x2 = 0 + 0.7 -1.1x + x2 = 0 + 0.7 Combine like terms: 0 + 0.7 = 0.7 -1.1x + x2 = 0.7 The x term is -1.1x. Take half its coefficient (-0.55). Square it (0.3025) and add it to both sides. Add '0.3025' to each side of the equation. -1.1x + 0.3025 + x2 = 0.7 + 0.3025 Reorder the terms: 0.3025 + -1.1x + x2 = 0.7 + 0.3025 Combine like terms: 0.7 + 0.3025 = 1.0025 0.3025 + -1.1x + x2 = 1.0025 Factor a perfect square on the left side: (x + -0.55)(x + -0.55) = 1.0025 Calculate the square root of the right side: 1.00124922 Break this problem into two subproblems by setting (x + -0.55) equal to 1.00124922 and -1.00124922.Subproblem 1
x + -0.55 = 1.00124922 Simplifying x + -0.55 = 1.00124922 Reorder the terms: -0.55 + x = 1.00124922 Solving -0.55 + x = 1.00124922 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + x = 1.00124922 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + x = 1.00124922 + 0.55 x = 1.00124922 + 0.55 Combine like terms: 1.00124922 + 0.55 = 1.55124922 x = 1.55124922 Simplifying x = 1.55124922Subproblem 2
x + -0.55 = -1.00124922 Simplifying x + -0.55 = -1.00124922 Reorder the terms: -0.55 + x = -1.00124922 Solving -0.55 + x = -1.00124922 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + x = -1.00124922 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + x = -1.00124922 + 0.55 x = -1.00124922 + 0.55 Combine like terms: -1.00124922 + 0.55 = -0.45124922 x = -0.45124922 Simplifying x = -0.45124922Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.55124922, -0.45124922}
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