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Simplifying (6x + 10) + (5x + -28) * x = 0 Reorder the terms: (10 + 6x) + (5x + -28) * x = 0 Remove parenthesis around (10 + 6x) 10 + 6x + (5x + -28) * x = 0 Reorder the terms: 10 + 6x + (-28 + 5x) * x = 0 Reorder the terms for easier multiplication: 10 + 6x + x(-28 + 5x) = 0 10 + 6x + (-28 * x + 5x * x) = 0 10 + 6x + (-28x + 5x2) = 0 Combine like terms: 6x + -28x = -22x 10 + -22x + 5x2 = 0 Solving 10 + -22x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2 + -4.4x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -4.4x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -4.4x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -4.4x + x2 = 0 + -2 -4.4x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -4.4x + x2 = -2 The x term is -4.4x. Take half its coefficient (-2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. -4.4x + 4.84 + x2 = -2 + 4.84 Reorder the terms: 4.84 + -4.4x + x2 = -2 + 4.84 Combine like terms: -2 + 4.84 = 2.84 4.84 + -4.4x + x2 = 2.84 Factor a perfect square on the left side: (x + -2.2)(x + -2.2) = 2.84 Calculate the square root of the right side: 1.685229955 Break this problem into two subproblems by setting (x + -2.2) equal to 1.685229955 and -1.685229955.Subproblem 1
x + -2.2 = 1.685229955 Simplifying x + -2.2 = 1.685229955 Reorder the terms: -2.2 + x = 1.685229955 Solving -2.2 + x = 1.685229955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + x = 1.685229955 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = 1.685229955 + 2.2 x = 1.685229955 + 2.2 Combine like terms: 1.685229955 + 2.2 = 3.885229955 x = 3.885229955 Simplifying x = 3.885229955Subproblem 2
x + -2.2 = -1.685229955 Simplifying x + -2.2 = -1.685229955 Reorder the terms: -2.2 + x = -1.685229955 Solving -2.2 + x = -1.685229955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + x = -1.685229955 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = -1.685229955 + 2.2 x = -1.685229955 + 2.2 Combine like terms: -1.685229955 + 2.2 = 0.514770045 x = 0.514770045 Simplifying x = 0.514770045Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.885229955, 0.514770045}
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