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Simplifying 15x + -10 = 4 + -10x(4x + -7) Reorder the terms: -10 + 15x = 4 + -10x(4x + -7) Reorder the terms: -10 + 15x = 4 + -10x(-7 + 4x) -10 + 15x = 4 + (-7 * -10x + 4x * -10x) -10 + 15x = 4 + (70x + -40x2) Solving -10 + 15x = 4 + 70x + -40x2 Solving for variable 'x'. Reorder the terms: -10 + -4 + 15x + -70x + 40x2 = 4 + 70x + -40x2 + -4 + -70x + 40x2 Combine like terms: -10 + -4 = -14 -14 + 15x + -70x + 40x2 = 4 + 70x + -40x2 + -4 + -70x + 40x2 Combine like terms: 15x + -70x = -55x -14 + -55x + 40x2 = 4 + 70x + -40x2 + -4 + -70x + 40x2 Reorder the terms: -14 + -55x + 40x2 = 4 + -4 + 70x + -70x + -40x2 + 40x2 Combine like terms: 4 + -4 = 0 -14 + -55x + 40x2 = 0 + 70x + -70x + -40x2 + 40x2 -14 + -55x + 40x2 = 70x + -70x + -40x2 + 40x2 Combine like terms: 70x + -70x = 0 -14 + -55x + 40x2 = 0 + -40x2 + 40x2 -14 + -55x + 40x2 = -40x2 + 40x2 Combine like terms: -40x2 + 40x2 = 0 -14 + -55x + 40x2 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -0.35 + -1.375x + x2 = 0 Move the constant term to the right: Add '0.35' to each side of the equation. -0.35 + -1.375x + 0.35 + x2 = 0 + 0.35 Reorder the terms: -0.35 + 0.35 + -1.375x + x2 = 0 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + -1.375x + x2 = 0 + 0.35 -1.375x + x2 = 0 + 0.35 Combine like terms: 0 + 0.35 = 0.35 -1.375x + x2 = 0.35 The x term is -1.375x. Take half its coefficient (-0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. -1.375x + 0.47265625 + x2 = 0.35 + 0.47265625 Reorder the terms: 0.47265625 + -1.375x + x2 = 0.35 + 0.47265625 Combine like terms: 0.35 + 0.47265625 = 0.82265625 0.47265625 + -1.375x + x2 = 0.82265625 Factor a perfect square on the left side: (x + -0.6875)(x + -0.6875) = 0.82265625 Calculate the square root of the right side: 0.907003997 Break this problem into two subproblems by setting (x + -0.6875) equal to 0.907003997 and -0.907003997.Subproblem 1
x + -0.6875 = 0.907003997 Simplifying x + -0.6875 = 0.907003997 Reorder the terms: -0.6875 + x = 0.907003997 Solving -0.6875 + x = 0.907003997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + x = 0.907003997 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + x = 0.907003997 + 0.6875 x = 0.907003997 + 0.6875 Combine like terms: 0.907003997 + 0.6875 = 1.594503997 x = 1.594503997 Simplifying x = 1.594503997Subproblem 2
x + -0.6875 = -0.907003997 Simplifying x + -0.6875 = -0.907003997 Reorder the terms: -0.6875 + x = -0.907003997 Solving -0.6875 + x = -0.907003997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + x = -0.907003997 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + x = -0.907003997 + 0.6875 x = -0.907003997 + 0.6875 Combine like terms: -0.907003997 + 0.6875 = -0.219503997 x = -0.219503997 Simplifying x = -0.219503997Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.594503997, -0.219503997}
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