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Simplifying 2(x + -4) * 5x = 7 Reorder the terms: 2(-4 + x) * 5x = 7 Reorder the terms for easier multiplication: 2 * 5x(-4 + x) = 7 Multiply 2 * 5 10x(-4 + x) = 7 (-4 * 10x + x * 10x) = 7 (-40x + 10x2) = 7 Solving -40x + 10x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + -40x + 10x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -40x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.7 + -4x + x2 = 0.0 Move the constant term to the right: Add '0.7' to each side of the equation. -0.7 + -4x + 0.7 + x2 = 0.0 + 0.7 Reorder the terms: -0.7 + 0.7 + -4x + x2 = 0.0 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + -4x + x2 = 0.0 + 0.7 -4x + x2 = 0.0 + 0.7 Combine like terms: 0.0 + 0.7 = 0.7 -4x + x2 = 0.7 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 0.7 + 4 Reorder the terms: 4 + -4x + x2 = 0.7 + 4 Combine like terms: 0.7 + 4 = 4.7 4 + -4x + x2 = 4.7 Factor a perfect square on the left side: (x + -2)(x + -2) = 4.7 Calculate the square root of the right side: 2.167948339 Break this problem into two subproblems by setting (x + -2) equal to 2.167948339 and -2.167948339.Subproblem 1
x + -2 = 2.167948339 Simplifying x + -2 = 2.167948339 Reorder the terms: -2 + x = 2.167948339 Solving -2 + x = 2.167948339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 2.167948339 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.167948339 + 2 x = 2.167948339 + 2 Combine like terms: 2.167948339 + 2 = 4.167948339 x = 4.167948339 Simplifying x = 4.167948339Subproblem 2
x + -2 = -2.167948339 Simplifying x + -2 = -2.167948339 Reorder the terms: -2 + x = -2.167948339 Solving -2 + x = -2.167948339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -2.167948339 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.167948339 + 2 x = -2.167948339 + 2 Combine like terms: -2.167948339 + 2 = -0.167948339 x = -0.167948339 Simplifying x = -0.167948339Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.167948339, -0.167948339}
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